Let me give you a couple of examples: 1."From the preview, the movie didn't strike me as funny. But when I watched it, I thought it was hilarious!" 2. "He makes me laugh all the time. If you saw him on the street though, he wouldn't strike you as someone who is funny. He looks very serious most of the time." Explanation: When something "strikes" you, it is the impression it gives you. In the first example, the person did not expect the movie to be funny because the preview gave him the impression that it would not be funny (or, in other words, it did not look funny to him).

When something strikes me funny = When I find something funny = When I encounter something and think it is funny.

It means, "it impresses me as funny". "I find it funny." Luke gives some excellent examples. Generally, it implies that one cannot detail exactly why it left one with the impression 'it' did. 'To strike one as' can be use with lots of other adjectives. "He strikes me as foolish for having said that." "That sentence strikes me as bad English". (I'm not sure why but it doesn't quite sound right.) He strikes me as a kind person (not based on a particular incident but based on my general impression). I like this expression. It strikes me as useful for expressing how one feels.