Does Ray of Enfeeblement Stack with Itself?

You can cast it more than once on the same target, and the highest roll will effect it. It wouldn't stack, as it's just a penalty.

Does Ray of enfeeblement stack with resistance?

It halving the damage of the attacker and the Barbarian's Rage are two different things, so yes, it would stack. Only multiple resistances don't stack.

How does Ray of enfeeblement work?

A black beam of enervating energy springs from your finger toward a creature within range. Make a ranged spell Attack against the target. On a hit, the target deals only half damage with weapon attacks that use Strength until the spell ends.