At the end of each level (once you have went though the portal) must the bard return his tokens or do they continue to be in effect when starting a new level?

You jeep those on whatever cards have them, if any.

The only things that are reset between stages is the map and anything that is left on it when the heros leave.

Everything else sticks around.

(Familiars, Trap tokens, Monsters, Image tokens. These get reset)