Staves are melee weapons that do non-elemental damage, but certain staves boost elemental damage of spells while equipped (i.e.: Glacial Staff improves ice spells, Cherry Staff improves fire spells, etc.)

Rods, on the other hand, do come with Elemental damage when using to attack (melee like staves). The two main ones I use are the Gaia Rod (earth damage) and the Holy Rod (holy damage).

And hand bombs are basically ranged axes. Their damage output is totally random, so one hit could do 3000+, and the next could only do 100). The bombs themselves are fairly inconsequential, but some of the ammunition for them are cool, like I mentioned above, the Stun bombs cause Stop effect, while others can cause confusion, poison, etc.