Can anyone explain the difference between watashi and atashi? And what about anta and omae?
Watashi is the polite/gender-neutral term to refer to oneself. It's just all around awesome because you can use it in almost any situation. Atashi (same kanji as watashi, just read differently) is the feminine casual way to refer to oneself. It's usually used by young women.
Anta is the casual contraction of anata, with anata being the polite form of "you". It's sometimes used by couples to refer to each other. Likewise, omae may be used by friends or couples, usually coming from males. It's quite impolite/derogatory otherwise.