Q:

Were there any successful attempts by the Allies to "turn" groups of Axis soldiers?

Toward the end of World War II, Germany had to utilize non-German soldiers, some of them from occupied countries like Poland and the Ukraine. At places like Omaha Beach, Normandy, individual Poles spontaneously defected, particularly when spoken to by Polish-Americans.
On the eastern front, the Germans managed to "turn" a whole division or more of captured Soviet soldiers under General Vlasov into fighting for the Germans against the Soviet Union.
Were there cases of the Allies seeking and receiving the defection of groups of soldiers recruited by the Germans (or Japanese)?
I'm excluding Italians (except when in German, not Italian uniform), since Italy itself was successfully "turned" by the Allies. Ditto for Vichy French soldiers in North Africa (unless in German uniform).

A:

I've promised to write an answer regarding Poles from Wehrmacht who joined Allies. So here it is.
Polish soldiers in Wehrmacht
First, how did Polish people land in Wehrmacht? There were three kinds of them. First of all, there was German minority living in Poland before the war (Polish citizenship). Second, Polish minority living in Germany (Polish nationality). Those groups had small or no choice to avoid army service, also many of them could actually believe and support Hitler. 
But the third group was the biggest. Poles of both Polish citizenship and nationality, who singed Volksliste - the special document stating that they are Germans (if they lived in particular regions of Poland that had strong historical connections with Germany). Some of them made it because they found it an opportunity for themselves, others were simply forced to do that (many of those who didn't sign it, landed in concentration camps or had other problems). 
Dates and numbers
From the overall number of 225000-375000 Wehrmacht soldiers, depending on how you define being a Pole, 90000 joined Polish Armed Forces in the West between 1943 and 1945. That's why I don't agree with the use of word "individual" in your question.
But I'll agree that from every German unit only individuals decided to do that. Why? The reason for that is because Germans perfectly knew they can't trust Poles. They didn't organize military units that based on Polish soldiers, but instead pushed few of them to each unit. So in fact, there were only Polish individuals in every German unit. Also any kinds of indiscipline, tries of desertion or acts of sabotage were punished with death. Still, some of them decided to do that.
I won't talk here about the history of Polish soldiers fighting together with Allies, as it's a different matter. Let's just say that the cooperation started in France in 1939, followed by 35000 soldiers coming to Great Britain, making up the largest non-British contribution in Battle of Britain.
Together, Polish Army Forces in the West counted around 220000 people (without counting the 30000 in reserve). There were also Home Army (biggest resistance movement in WW2) and Polish Army Forces in the East, but it's another topic.
So the mentioned 90000 soldiers from Wehrmacht made 40% of the overall number. Where and when they were recruited?
Before the Normandy, during North-African campaign, 2000 Poles from Wehrmacht were recruited. In the Middle East (1943) and Italy (1944), additional 2500.
As for the time between Normandy and the end of 1944, the number is 29000 (half by half for western and southern front).
1945 brings 55000 Polish soldiers from Wehrmacht joining Polish Army Forces in the West. Unfortunately, because of the ending stage of war, it's difficult to say how many of them actually took part in any fights.
It's important to add that there would be much more of them before 1944, because of the situation at Eastern Front, but Stalin didn't agree to release Poles from Wehrmacht kept in his prisoners-of-war camps. Later, many of them joined Polish Army Forces in the East.
Normandy as an example of recruitment practises
So what was the way of recruitment? Thankfully we have a good overview of that. As you've already mentioned Normandy, let's take it as an example. On the way, I'll explain why I don't agree with the use of "spontaneusly" and "Polish-Americans".
Polish forces, already having experiences from the Mediterranean front, perfectly knew what to do and that there will be great amount of Polish people who want to join Allies. Long before, the advertising campaign started, organized by the Polish government in exile, using a.o. flyers and radio messages. This way for many Poles from Wehrmacht who decided to join Allies, this decision wasn't spontaneus at all. They already knew before the battle, what they're going to do.
Here's the text of this message, written by the Minister of Defence, gen. Marian Kukiel,  but translated by me from Polish language original, so all the language awkwardness is mine:

POLES IN GERMAN ARMY! The violent force pushed you among the ranks of
  deadly enemies of Poland, who abuses our Nation like a torturer. The
  violent force made you to wear German uniform. They order you to fight
  with armies of free nations (...). Together with Americans, Britons,
  Canadians and Frenches, there are also Polish Army Forces fighting.
  Many of you already got the guidelines, what Poland expects from you.
  The Government of Poland orders you: Don't shoot to your brothers -
  allied soldiers. If you have to shoot - miss the target. On the first
  opportunity go on Allies side or hide yourself, until they come for
  you. Serve Allies with all informations, when you meet them. When
  you're among the Allies, report that you're Polish, ask not to be kept
  with German prisoners and instead ask for contact with Polish Army
  officials. Your brothers, fighting together with Allies for
  liberation, want that from you. Long live Poland!

The (...) is there because I failed to translate a short part. The "violent force" is literal translation of "przemoc", which is a clear reference to words of Polish national anthem, which translated to English are: What the enemy's force has seized, we'll take back by the sword.
Recruitment in camps
So now imagine you're a Pole in the prisoner-of-war camp, right after Normandy. Of course the morale is at the lowest level which means completely no discipline. All Germans are angry with you, blaming Poles for not fighting. Allies realized what was happening, so in some camps, they arranged separate places for people of different nationality. But until it happened, they didn't want to interfere. So you could only stick together as a group of Poles, for better protection, until somebody came and took you out. 
In this situation Polish officials had to act quickly. So Polish officers were coming from place to place and talked with soldiers about Polish Army Forces, offering joining them and fighting for liberation.
Now as for "Polish-Americans", mentioned by you. Of course there were around 2000 Polish-Americans who came fighting from United States and joined Polish Army Forces in 1944/1945. There also surely were some of Polish-Americans with American Army. But I don't think any of them had higher rank or any reputation, especially that American soldiers lacked experience and it was just the beginning of their campaign in Europe. And on the other side there were Polish Army Forces full of officers, already with big successes, fighting from the beginning of the war, on all fronts (they came from Russia through Middle East to Italy), who could easily turn Wehrmacht soldiers to fight for Allies. In this situation, who would care for Polish-Americans?
Of course I don't suppose you thought about Polish-Americans trying to convince Poles to join Allied forces in the middle of battle, with bullets swinging above the heads. :)
Investigation
Those soldiers who agreed, landed in special camps in Scotland (Hamilton, Johnstone, Findo Gask), England (Grimsby) and France (Cherbourg, also Polish sector of St. Raphael camp). There were also camps in Italy (Taranto, San Basilio), but served for other Polish soldiers, not from Normandy and western campaign. Those camps were only for Poles and guarded only by soldiers from Polish Army Forces, as it was part of the agreement.
Group after group, they were later sent to Polkemmet in Scotland (speaking of the western camps), for closer look. Polish officials were checking their health, abilities and most importantly, if they were really willing to fight for Poland. For example they were checking the soldier's rank in Wehrmacht. The lower it was, the better for the soldier (as any Pole with higher rank could be in fact on the Hitler's side). Also they were checking if particular soldier had anything to do with SS, which was hated by all Poles from obvious reasons.
There was a case of a Polish soldier from Waffen-SS, who succeeded to hide it and claimed that he served in Wehrmacht. Nobody found out about it until the end of the world, while the soldier received a high reputation among his new combat friends for killing Germans.
Consequences for soldiers
Now another interesting thing. What was important for the soldiers was the fact that from that time, being officially deserters from Wehrmacht, they were no longer under protection of Geneva Conventions. So in order to protect themselves and their families, every soldier had a new pseudonym. Of course there was small probability that a such soldier becomes recognized by Germans as previous Wehrmacht member, but there were such stories, the first one noticed in June of 1940. That led to the situation where many of them, who died in fights, were buried under false names around cemeteries of Europe.
Back to the front
The overall level of such soldiers was different. Of course all of them had already their military training and experience, so they didn't need another one and could be sent directly to the front. Many of them had even some good habits from Wehrmacht, f.e. regarding discipline and neatness. As pretty much everywhere, they were of different abilities. Some of them were excellent soldiers, while some others rather poor ones. Among the best ones there were soldiers from famous Fallschirm-Panzer Division 1 "Hermann Göring". Also mechanics from Luftwaffe had great abilities because of special trainings.
Of course at the beginning it was difficult for Polish regular soldiers to trust those who served in Wehrmacht. But later, especially when more of them came and in many units there were more than half of ex Wehrmacht soldiers, people stopped thinking about it.
In overall, Wehrmacht soldiers made a good addition to Allied forces. It's was nicely described by one of Polish veterans, who said that "it was Wehrmacht itself who conquered Bologna for the II Corp" (Bologna was the last act of Italian campaign in April of 1945).
That's all from me, as it's 3am here in Poland. I live the rest of nations for others.

A:

It appears that this happened with two units of the 30th Waffen Genadier Division of the SS. This division was recruited in Warsaw and was mostly peopled with various stripes of Slavs who happened to be anti-communist. 
This worked OK on the Eastern front. However, when transferred to eastern France to fight the Free French, two battalions shot their German commanders and defected with all their equipment to the Free French side.

