If you are delayed by a monster during the movment phase (like a child of the goat), what happens if you draw an encounter card that gives you the option to move to another location (like moving from the historical society to the woods to do bird watching)? Can you move while delayed or does the encounter not happen?

avec said:

Well, there is again the problem of interpreting what "delayed" means. In the rules, delayed means you do not receive any movement points, but you do all the phases anyway (including the Movement phase, during which you can cast spells or pick up clues). Therefore, even if you are delayed, you can fulfill an Encounter action, and I think it is possible to be transferred to another place.

To confirm this, in the FAQ, there is a similar case, showing you can be transferred to another location through an Encounter while being delayed:

Q: If an investigator is delayed in the Other Worlds and
draws an encounter that returns him to Arkham, is he
still delayed when he returns?

A: Yes. Returning to Arkham doesn't affect the fact that he is delayed.

I'm on board with Zeb. You still go and get your encounter (or enter a gate, if one's there), but you're still delayed .

Yep, you move. You just don't change your staus. So you remain delayed in your new location.