If you use Last will and launch all 4 goats, do you get 4 monsters, or do you get 1, or none at all?

You can't use Last Will with a sheep token. The tokens never go to the Graveyard, they are removed from play. Therefore you would fetch no monsters.

Like stated by Metra Mage before you can't as tokens never hit the grave, now in any case that you launched 4 other monsters you would only get 1 monster by Last Will's effect... unless you used 3 Last Will's then youi'll get 3, its a 1 4 1 trade

Just to clarify a bit since your example can be taken in different ways...

If you activate 3 Last Wills and then you have 3 monsters that go to the grave, you DO get to summon 3 monsters from your deck...HOWEVER, you don't get 3 monsters from your deck because you sent 3 monsters to the graveyard. You get 3 monsters right after the FIRST monster goes to the grave. The second and third monsters do nothing for the Last Wills that were previously activated.

Last Will creates a state that lasts for that turn until a monster is sent to the grave. If you activate 3 Last Wills, then each creates that state, and when a monster is sent to the grave, then all 3 Last Wills' effects kick in and you get 3 monsters for that 1 that was sent to the grave, one for each Last Will.