1. Watashi (私) is the general word for "me" or "I." It's used by both male and female but is only used by females in colloquial situations. For example, if a female is talking to her friends, she would refer to herself as 私. On the other hand, 私 is only used by males in FORMAL situations. So, when a male is introducing himself to his coworkers or boss for the first time, he would refer to himself as 私. However, it's pretty unnatural for a male to refer to himself as 私 in casual situations.
2. Boku (僕) is used by grown men and little boys. When men use this word , it's usually in formal settings, and they place emphasis on the KU of "boku." There is a difference between "boku" and "watashi" because the former more masculine and is friendlier and warmer than the latter. This word is also used by little boys in casual settings, but in this case, the BO of "boku" is stressed. It's a very cute word when a young boy uses it, but it would sound unusual for a teenager to use it. Also, the word "boku" is used by both sexes in songs.
3. Ore (俺) is a VERY casual way for males to refer to themselves. It's extremely masculine, so people only use it in casual conversations. It's not rude at all and is actually extremely natural for men to use it. However, if a woman uses this word, she is considered to be lacking in etiquette because she isn't "lady-like." haha but my cousin, who is a girl, ALWAYS refers to herself as "ore" because she's just weird like that.