All of these are more or less synonymous, but I have most often heard 復活する and 蘇る.
復活する means "to come back to life" in both the literal sense and the metaphorical. For example, if you are really tired from work and later eat a good meal and start to feel more energetic, then you could say 復活した！
蘇る is used in more spiritual situations, I believe. I often see it in video games and it means "to be resurrected."
生き返る I have also heard, but not nearly as often as the two above. I think it's meaning is probably closer to 蘇る.
I don't think Japanese people always care to use all these variations and in Japanese there are often words with similar meanings, but slightly different nuances, so you have to be careful about that. In this situation though, I think the differences in usage for these words would be a matter of preference and perhaps used for literary expression, than for anything practical. Japanese is a very flexible language and has thus come up with numerous different ways to express the same thing.