Wands seem easy to understand. If you have the spell on your spell list, you can use the wand.
What about staffs? If I have some of the spells stored in a staff on my spell list, can I use the rest of them?
I haven't found any rule in staff section that would override general spell-trigger rule that to activate spell from spell-triger item you have to have that particular spell on your spell list. Thus you can only use spells that belong to your class and cannot use other spells, even if staff contains both types.
Drejk is correct. Your options are have the spell on your class list or UMD.