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How does being an immigrant effect acceptance chances into law school. For example, I was born in the form USSR and immigrated to America. Will that give me any kind of advantage when it comes into getting into law school. One of my law professors was telling my classes that law schools love to diversify. What do you guys think?

I think it would depend on how long you have been here. If you came when you were 5 you are essentially an American and I doubt it would matter but if you just came 5 years ago and have an interesting story I think it could be added to your "soft" factors.

So how does this look
3.7 GPA at the end of this semester. Economics. I started really, really poorly, my freshman year. I had a D in calculus and C in music. I've been consistently getting A's and
Didn't take the real LSAT yet.
Immigrated at 15 from the Ukraine
No extra activities other than Student Government.
Multi-Lingual

I was also born in the USSR and emigrated to the U.S. at a young age, but I do not think it had a measureable effect on my cycle. I used my family's experiences for the diversity statement, since it does provide some interesting context for the rest of the application. I would be sure to incorporate it somehow, yet do not expect law schools to treat you like a URM. If nothing else, you become a more unique applicant with a distinct perspective to offer. Is it enough to pad your LSAT, etc.? No, but some admissions personnel might empathize with you and give your application a bit more attention.

You sound pretty average for the T-14 but since you immigrated at an older age I'd say you have a pretty nice PS or Diversity Statement. No real boost though.