You might be right about Tulkas and Orome possibly fighting in the War of
Wrath. If any Valar would have come, those two would have been at the
head of the line and would have been the most likely. I guess the fact a
Maia was the commander is my main reason for speculating that the Valar stayed
home, that and the somewhat half-hearted efforts to clean up afterwards as
outlined below!
On your Sauron question, in "Of the Rings of Power and the Third Age" it says
that at the end of the War of Wrath Sauron humbled himself before Eonwe, but
was miffed when he was told he had to back to Valinor for judgment from the
Valar. Then Sauron hid and since he was wearing his fair disguise after
Morgoth's fall, he was able to do a lot more damage in the Second Age. At
the end of the War of Wrath, though, Sauron was forgotten in the rush to go
back to Aman. It does seem as though a lot of the mop-up is pretty poorly
planned, and of course a huge chunk of ME has completely vanished, leaving
everything in upheaval. The War of Wrath looks like it was pretty much a
one-time intervention and once Morgoth was crushed, the victors left a lot of
mess behind. If they had done a better job particularly of capturing
Sauron, think how boring life would have been in the next two ages! And
of course, there would be no LOTR
either.
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"The world is changing: I feel it in the water, I feel it in the earth, I smell it in the air"
--Treebeard