I would only paint the trim in semi, the ceiling and walls in eggshell would be fine. You will need to lightly sand the semi gloss and it would not hurt to apply a quality bonding primer as well.

"Would it be odd to paint the ceiling an off white in semigloss and the walls in a different color in Eggshell? Or should I do the ceiling in Eggshell as well."

I have read that to have better light reflection from the ceiling (rather than absorbing light), painting it with white semi-gloss helps particularly in a smaller kitchen with less ambient light. I have not done this myself; just noted it as a possibility. Good luck.