If Osiris is traveling with a troop does he grant the combat powers of the alliance again on top of what they already get by default? For example, if the green player has the beastial fury tile, does he gain +1 from the tile and +1 from Osiris?
No. Osiris gives somehow to the linked troop all the different battle powers that the troop does not have yet.
Let's say :
Red has carnage (red lvl 2 : +1 damage in battle).
Osiris is linked to a full green troop. That green troop gains +1 damage in battle.
If Osiris is linked to a red/green troop, that troop gains "only" +1 damage in battle (not +2)
Consider that having Osiris in your troop is like having a mixed troop with all the colors of the alliance.
Hope I'm clear enough