I don't like chocolate ice cream much.
I don't like Vince Vaughn movies much.
I don't like hiking much.
I don't like hospitals much.
In all four of these cases, I would take it to mean that the person doesn't particularly care for the named item or activity. This could be anything from a moderate or mild dislike to a more moderate disinterest. In other words, perhaps this person has a genuine dislike for chocolate ice cream, but more likely they simply prefer other flavors over chocolate. Perhaps this person avoids hiking entirely, but maybe the person wouldn't mind going on a short hike a couple times a year. I wouldn't want to make too many judgments bases on such a vague statement, but I will say this: I wouldn't expect this person to be hitting the hiking trails every other weekend and ordering chocolate ice cream at that quaint little store near the end of the trail every time. But if the choice was between chocolate ice cream or no ice cream, it's difficult to know which way that might go based on the one statement alone.
It's hard to say whether the "much" modifies the thing or the degree of (dis)like because the expression is somewhat idiomatic and flexible in its application.
As others have said, one of the expressions in your first line ("I like it not much") is not really idiomatic and wouldn't be said by most native speakers.