I recently discovered that staffs can be dual wielded. Iwas messing with a charatcer that is heavy armor and dual destruction staffs but it's not easy. I know that I need a LOT of soul gems, but my real problem is that the staff damage doesn't seem to increase. I like the DoT staffs, like flames and shock as well as Flame Wall, but the base damage is always low. Without modding, is there a way to raise the damage like when you raise a weapon skill?

I don't think so,unless you find a more powerful staff to enchant.:/ sorry

The higher your character lvl the higher the lvl of the staff's you can find/buy.

Just be like Gandalf, and stick a sword in one of those hands.

Staffs correspond to their respective school of magic. So, a destruction staff will be more powerful if you have a high destruction skill. However, staffs will not raise your magic skills. It's not really intuitive, but if you want to use staffs effectively you'll also have to use regular magic. I think staffs are designed to be backup weapons for when you run out of magicka to cast regular spells you can rely on a staff.

A staff's power & number of charges are affected by the character's level and perks, on the corresponding magic school. They're also affected by fortify magic school enchants and potions.

As for soul gems, Azura's Star and soul trap will become your best friends.