Question: I'm looking to build strength. I'm not concerned with size or bigger muscles so much as strength.

At the moment I eat a lot of meat and carbs. For most meals I tend to eat things like donor kebabs, burgers, chicken, pizza, subway subs etc.

A lot might be considered junk food, although a lot is freshly made from decent restaurants. 

From what I understand protein is what is important for strength building. Is a high meat diet good for this? Does it matter if the meat comes from junk food sources, e.g. a quarter pounder from McDonalds?

Answer: 
If your only goal is strength, and you are getting at least 1g protein per pound body weight, then all the extra calories will be used for energy. Whether you use fat or carbs, your body still uses those macronutrients for energy. This sounds quite compatible with Mark Rippetoe's view on dietary requirements.

I think in many ways Rip's recommendations are overstated, because if you eat a lot more than you need, you will gain a good amount of fat along with your new muscle. That in turn makes it hard to move, and use your strength. To help keep things in balance, make sure your exercise has the following components:

* Strength (low rep, high weight)
* Hypertrophy (high rep, low-to-medium weight)
* Conditioning
* Mobility
* **Rest** (cannot be overstated)

Whatever it is you are focused on, you simply prioritize that component in your programming over the others. However, you should have all of the components to be truly successful. The conditioning and mobility will improve your ability to perform and use your strength on demand--as well as learn new techniques.

If you keep your strength portion focused around the four main compound exercises--overhead press, deadlift, squat, and bench press--and your assistance exercises in the hypertrophy range, you will do really well.

Basically, if you gain weight too fast, you will need to adjust the way you eat. Gaining too fast means you are gaining more fat than muscle. One way to do that is to have a protein shake before each meal. It keeps your protein up, and helps fill you up before you start diving in to the fast food.
If the sole goal is gaining strength, the source doesn't matter so much. If you're getting 50 grams of all the essential amino acids (most meat covers this) then you're fine.

The caveat is fast food has a lot of bad side effects. Your cardio will improve when you drop the McDonalds.