In Yggdrasil, which character abilities are most useful/effective?
Yes, there are tiers.

In order of effectiveness and efficiency:

Frey - 33% more actions than any other god, can excel either as pointman, support, or solo, since his play engine is self-sufficient

Thor - always present combat bonus gives great advantage for two worlds, Asgard and Jotunheim; less need for Nidavellir, Alfanheim, and Midgard

Tyr - better combat ability; reroll can affect a number of enemy effects (Fenrir, Jormungand, Hel, Surt); less need for Nidavellir, Alfanheim, and Midgard

Freyja - very situational advantages; otherwise, no direct efficiency bonuses:

-- can upgrade weapons faster than any other god, which lets other gods equip weaker versions on their turn, since gods cannot get equipment unless the next version is available, great for early attacks

-- double Midgard to get over a sunken island on her turn is more cost efficient than using the Vanaheim track

-- double Niflheim to re-distribute elves and vikings quickly

-- can pull off miracle saves for when three enemies cross the line for defeat conditions, by pushing back two enemies on Asgard and then using the Vanaheim track for the third, a feat that not even the mighty fighter Thor can do

Odin - only better if he comes before Tyr in the play order, to manage enemy effects

Heimdall - drains the viking pool too quickly after cleaning the white/blue bag; three enemy effects shut down his power very easily

With fewer players, usefulness of Freyja's ability decreases, usefulness of Frey's ability increases

With more players, usefulness of Frey's ability decreases, usefulness of Freyja's ability increases (due to weapon sharing restrictions)

See this thread on BoardGameGeek titled The powers of the gods - Odin awfully unmighty? Frey the best of all?