1. Put the vegetable mix on the gas stove.

Question

2. Put the vegetable mix over the gas stove.

3. Put the vegetable mix on the gas range.

4. Put the vegetable mix over the gas range.

(Which ones are grammatical? Which preposition do I have to use?)

Answer 1

1 and 3 are grammatical. As for the difference between range and stove, http://answers.yahoo.com/question/index?qid=20080322160757AACWRwb
has a good explanation.

Americans would probably be more likely to say "the mixed vegetables" than "the vegetable mix".

Answer 2

Putting it "on" the stove would indicate placing it on the surface of the stove. Putting it "over" the stove would indicate holding it above the surface of the stove.

I hope this helps a little more. Thanks for asking.