To strip a goblin of just their weapons, you need a bookkeeper who has been working with at least some degree of precision. Go into the (z)Stocks screen, scroll down to the Weapons category, and go through marking every goblin weapon for dumping. Note that there isn't necessarily an easy way to tell what weapons are goblin weapons and which aren't, though if your own weaponry is all high-quality or steel that works reasonably well. Dwarves will go to the goblin cages, take out the weapons, carry them to a garbage dump zone, and put them there.
To strip a goblin of weapons and armor, use the d-b-d mass dumping designation cursor. Designate the tile the goblin's cage is in for dumping. This will mark every item in that tile, including all of the goblin's equipment, for dumping. It will also mark the cage itself, though, which is undesirable, so, using the loo(k) cursor, go to the cage itself and remove the dump mark. As before, dwarves will go to the cage, take items mark for dumping out of it, and take them to a garbage dump zone.
Once a goblin is disarmed, there's a couple ways of getting them into an arena.
The first is to channel out the ceiling of the arena, designate the open space so created as a (i)zone set as a (p)it/pond, then use the (P)it information submenu off of there to set the goblins to be dropped in. Dwarves will go to the goblin cages, take the goblins out, drag them to the pit, and toss them in.
The second way is to build the cages in the arena, link a lever to them, then pull the lever. The cages will open, releasing the goblins, once the lever is pulled.