Question: Kind of a "universal donor" or "universal recipient"? Aliens that can take on the qualities of several kinds of species and recombine them to make a kind of "super" being?

Answer: 
Sorta yes. It may be possible, but not likely.

One issue is that we don't know if all life would be the same handedness. There is no reason it should be, in fact it should be about 50/50. How much the handedness of compounds matter can range from not mattering at all to being very potent toxins where if you expose someone to a compound that is left handed it will really be beneficial, but if its right handed it will kill them instantly.

But let's say all life works on basically the same RNA/DNA system. Well, then you're pretty much down to the programming analogy. Basically, there is no reason for some 4 bits to be one command and another be a different one. You're just randomly asigning them, but all PCs can run most OSs because they all use roughly the same base level command structure. Assuming there is limited amount of options for what those biological commands are (which as faras I can tell that is the case) then it should be possible to give birth to a given species by alien species (ignoring other issues). As in if bob the human mated with Susan the martian, susan could give birth to a human, but she could not give birth to Human-Martian hybrid from just this, because the commands are only for a human or a martian, not both. 1 BIOS can run at a time and 1 OS can run at a time...

So how do you get a hybrid? Shells. You can run a shell program which allows you to run another BIOS/OS on the same computer while running the main OS. The Shell OS can make alteration to the files and such just as the main OS, but the main OS is in charge and also you are expending more resources to run both. Is this possible with biology? I see no reason why not.

So you'd then get a hybrid Martian-Human, but the Martian would be dominant to the point where you might as well not call it a hybrid.

The alien from the movie Species and the Asari from Mass Effect both seem to work in outward appearance similar to this.
On its own, no.
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* Genetic material is not compatible. DNA is not compatible with structures of not only different chemicals, as would likely be present, but also different, non-helix shapes, making the combination of genetic structures **extremely improbable if not statistically impossible**.
* If the genetic material is somehow adapted by exchanging most of the molecules for compatible chemicals, and changing the shape (which your organism, however complex, probably cannot do), the genes produced will not have the same meaning to decoding enzymes or machines. What may mean blue eyes for species A could be decoded as an exoskeleton for species B.
* If you make the genetic molecules compatible, and make sure the genes represent what they are supposed to do, the offspring will likely be grotesque and
malformed. Cross a human and a cow and you will **not** get
a cow with a human head or a human with udders. Things will mix in a
number of unpredictable ways and kill the organism. Picture a human with a compartmentalized stomach, fur, a skewed metabolism, and a circulatory system that doesn't go through the entire body, effectively killing the creature at birth.
* If the body somehow functions, which is **very very unlikely**, the brain still probably won't. It will not have regions corresponding to every organ in the body, as a random combination of genes means not every organ gets representation. Additionally, it may have redundant regions that evolved to control something that this hybrid creature doesn't have.
* Finally, if all of the above conditions are met, and through impossible statistics, the organism is able to develop and survive, it will die in utero. The mother organism will create the child using the nutrients it knows how to process for *its own kind.* It will not process the nutrients the other organism inside of it needs to grow effectively.

However, complex machines can always solve your problems.
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