Crave means to desire something (usually food) strongly. An example is "women often have a craving for chocolate" Or "pregnant women get weird cravings to eat pickles and ice cream. In the song, Alanis wants, craves the person or relationship she's singing about, the "object".
As for the other words, I have no idea. Probably some underlying meanings. I would say use a search engine to find an Alanis Morrisette fan club page and ask them there!