There are several words in there I did not know and many others used in a different sense than today's. I'm still not sure but here you go. First draft (based on Roberto's text):

A vulture(Geyer) has flown out from Hegau near the Black forest (Hegau is roughly the region between the lake of Constance and the Southern Black Forest),
who(which) has grown a lot of young, namely the peasants everywhere (only with this half line, the double meaning is narrowed down to Florian G.).
They have started to rise up in the German nation
and have their own order (community) they possibly may fare well (prevail).

I now talk about the peasants and their rule (old meaning of ‚regiment’)
Some may call them rogues (I didn’t know ‘Lauren’ but found it means ‘Schelme’) and don’t know the end
(a bold guess for ‘Schinder’ and ‘Schaber’ being instruments with which the peasants fought:) you can see skinning knifes and scrapers at work in high spirits
Pay attention, you extortioners (profiteers) it will not be good in the long run.

They scare the power/rulers (‘Herrschaft’ is both the power and the people who have it) so that they (the rulers) hardly know where to go
They wake up the peasants and (‘nemens nach der Baus’ = ‘jemandem zusetzen’) and go for (the rulers)
They are uncommon vagrants (‘Kunde’ today = customer, then in the sense of ‘Landstreicher’) they dare their skins (= risk their lives)
They found a sense (a common aim) who would have believed them capable of that?

They went into battle and none of them backed off
It’s true and no lie, many a peasants’ boy (a quite late explanation of who the ‘they’ are in the first line)
They have sworn together to make the aristocracy suffer (‘harm’ would today be a better translation, the word ‘Leid’ has lost a lot of strength since then)
They nearly skinned them (the aristocracy), what will be their prize/fate? (the second ‘geschworen’ on Frank’s website must be a typo for ‘geschoren’; I’ve used the stronger ‘skinned’ instead of the verbatim ‘shorn’)

The farmers have united and wage war with violence
They have a great order (in a secular sense: a community with a common aim) and rebel at many places
And they tear the palaces apart and burn the cloisters/monasteries down
So we cannot be screwed (ripped off) any longer, (freely and boldly now:) who cares for the evil castles of robber barons?

Das buendisch Liedlein (scroll to second song to find the old tune to this song). (Is that the tune on the recording, Roberto?)

BTW, Martin Luther commented like this:
The ass wants to be hit and the rabble needs to be governed with brute force. The peasants do not want to listen to common sense and therefore their ears have to be forced open by clubbing them with box-tree clubs until their heads jump into the air.

Wolfgang