There are no invincible squads. Don't grow over-confident in using them, or they'll all die horribly.
Perhaps not, but legendary +5 wrestling combined with legendary +5 shield use and superdwarvenly tough comes very, very close. I've had a single champion devastate whole goblin sieges including archer squads without a scratch, and even the whole non-SoF HFS (though he did get a few minor wounds from that).
The only realistic way such a champion could die is an insanely lucky arrow shot or so many enemies he passes out from exhaustion fighting them all (and even then you can block while passed out so it would take a while to kill him).
Probably the most realistic way, and probably more often that you think. I mean, I had a guy firing off his bolts in pretty well crafted armor, legendary in armor, crossbow and wrestling at a goblin bow squad. He killed them all, but the last guy managed to fire off an arrow that hit and got stuck in his throat. He took a few steps back, collapsed, and bled to death.
What are the freaking odds?!
Melee units are no threat to champions (unless there are like.. a million of em? Though I've seen a video of a dwarf champion taking on a
lot of enemies. Estimate 200 enemies.) but the crappiest goblin bowman can do serious damage.
Remember to assign war dogs early, because when they reach hero/champion status, they can't be assigned anymore (and I hope that's going to be fixed in a later version).