It is possible to block with one handed weapon as long as your left hand is empty. You cannot block while dual-wielding.
Blocking is slightly less effective with a weapon than with a shield. With 0 blocking skill, a weapon blocks 40% of damage while an iron shield blocks 50% damage. At 100 blocking skill, a weapon does 60% damage reduction, while a daedric shield does 63% damage reduction. Blocking with weapons benefit from the shield wall perk at the bottom of the block tree.
Bashing with a two-handed weapon does more damage than bashing with a shield. With deadly bashing perk, daedric warhammer does 102 damage, while daedric shield does 68 damage.
You cannot block arrows with a weapon.