What do you do if someone uses part of your answer and gets points for theirs? Shouldn't I be able to get part of those points? Or is this an "honor" issue and the person who used your answer is not being honorable? Can you report it, or should I even care?
The best thing to do is probably to just let it go. However, there are a couple instances in which you might not want to:
Be wary of the second one - I wouldn't flag if it's just a copied sentence, but if it's a paragraph or some such, then continue.
In either case, if the situation is appropriate, flag for moderator attention under "it needs ♦ moderator attention" - use the "other" reason, and explain (in some level of succinct detail) what you think is going on.
It's hard to answer this without your definition of "uses part". "uses part" could mean:
Number 1 and 2 can cause issues. If someone quotes a sentence or two from one of your answers with proper attribution, that's OK. Otherwise you should probably flag the answer explaining the situation.
3 should definitely be flagged (make sure you include a link to your answer!)
For 4... Well I'm just going to quote an old joke someone told me (I forget exactly where I heard this..):
So, if he just happens to have some identical code from one of your answers, he may very well have come up with it on his own. Unless it's a lot of code, I'd just let it go.
Also remember, content posted on Stack Overflow (and all other Stack sites) is posted under the CC-wiki license. So
A. You don't really "own" the content you post, and
B. Anyone can copy or reproduce it if they want (they are supposed to attribute it though)