Both are not good, they look like just a part of a sentence.
много = many, a lot of
очень = very
If you say "я изучаю очень/много" you need to finish your thought: I study a lot of/many ..." (what?), "I study very..." (how or what?)

Better examples:
Я изучаю очень трудный предмет (I study a very difficult subject)
Я изучаю много разных языков (I study a lot of different languages)

If you wanted to say "I study a lot" (as in "I put a lot of time/effort into it") you can say "Я много занимаюсь" or "Я очень много занимаюсь".