If you have Viscera Dragger in your yard, and then Unearth him. Then later that turn Cycle a card and Astral Slide out Viscera Dragger, does he return to play at EOT? If so, I assume that would make him stay in play and not retrigger unearth.
for referance:
Unearth


(


: Return this card from your graveyard to play. It gains haste. Remove it from the game at end of turn or if it would leave play. Unearth only as a sorcery.)
Astral Slide:
Whenever a player cycles a card, you may remove target creature from the game. If you do, return the removed card to play under its owner's control at end of turn.
From the comprehensive rules:
502.84. Unearth
502.84a Unearth is an activated ability that functions while the card is in a graveyard. “Unearth [cost]” means “[Cost]: Return this card from your graveyard to play. It gains haste. Remove it from the game at end of turn. If it would leave play, remove it from the game instead of putting it anywhere else. Play this ability only any time you could play a sorcery.”
From the FAQ:
If a creature returned to play with unearth would leave play for any reason, it's removed from the game instead -- unless the spell or ability that's causing the creature to leave play is actually trying to remove it from the game! In that case, it succeeds at removing it from the game. If it later returns the creature card to play (as Oblivion Ring or Flickerwisp might, for example), the creature card will return to play as a new object with no relation to its previous existence. The unearth effect will no longer apply to it.
To answer your questions:
If you have Viscera Dragger in your yard, and then Unearth him. Then later that turn Cycle a card and Astral Slide out Viscera Dragger, does he return to play at EOT?
Yes, he returns.
If so, I assume that would make him stay in play and not retrigger unearth.
Correct, a zone change means the card is a new object and won't be tracked by delayed triggers like unearth.