Been using mostly aggro decks because I think they're the most fun, and seem to have the best success when played against a significantly stronger deck (have beaten several decks with tons of orange cards and insane spells with a level 5 aggrodin).

yet, Priests seem to shit all over me. I can't handle their heal and strong damage individual cards at mid-late game. I have to sacrifice my entire board to take out one of their big guys because if I don't do it all in one move, he'll just heal him back to full... Then I've lost 2-3 cards for his 1 and he just drops another big card down.

I have some strong 8 mana cards, but I don't use them in my deck because I don't ever intend for the game to get late enough to use them, but against a Priest maybe I need at least one to have a hail-marry reach card for late game? (I managed to find a Gruul card, seems pretty strong?)

shockadin runs alot of 1-2 health guys and priests have lots of aoe and ways to deal 1-2 damage to the board..

just with any deck you have your good matchups and then you have your bad ones.. but against something like that if you try to tech in anti control cards like sylvanus or something like card draw your only hurting matchups that ur highly favored vs just take gain a couple % on an alrdy bad matchup so all in all not worth.

If you're playing an aggro deck then don't worry about trading into his minions. It's difficult for aggro to beat priest if they draw cards like Deathlord early. But typically you can ignore a card like Auchenai Soulpriest or Sylvannas and just push for face damage.

I think the big minions he's talking about are probably Belcher and Deathlord

If that's the case, get an owl.