Does the other weapon need to be offhand or can you give two of the same weapon to your toon to dual wield?
It depends. If the weapon is Lore then you can only have one of them. The mystical claws of Jojo linked above are primary only and offhand only. However, many weapons (especially crafted/mastercrafted) can be wielded at the same time.
Personally I prefer to use weapons of two different skills. My Berserker is using slashing and crushing and my Swashbuckler (who's also using the Jojo claws currently) normally does slashing and piercing. That way my skills are kept current with their max level in case I run into a new awesome weapon.