I have read this in the Version 1.2 Errata and FaQ:

"Q: When a large monster interrupts its movement to perform an action, does the figure have to be placed on the map in all empty spaces?

A: Yes, a large monster cannot interrupt its movement unless it can be placed on the map and all the spaces it occupies are empty spaces. "

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What is considered an empty space?

A space containing a search token/ objective token is not empty, so Monsters can not sit on these items at the end of their turn, correct?

or are the tokens treated as something else? if so, then heroes should still be able to search/pickup even though the space in which they are designated is beging covered by a monster.

Well scanning the rule book it doesn't say anything about search tokens and if the space they occupy is empty or not .

I have always played that a hero or monster could occupy the space of a search token.

If the search token is adjacent to a hero even if that space is occupied by a monster, you could perform a search action.

I think you could "greedy" a search token 3 spaces through a monster because those are still countable adjacent spaces.

Also the familiar "Skye" from the CK technically occupies a space but it has been confirmed in the FAQ that if a monster ends his turn(1space monster) then Skye's ability is negated.

Page 9, top left:

Empty Spaces
Some card effects and abilities refer to empty spaces. An empty space is defined as a space that contains no figures and that blocks neither line of sight nor movement. Unless otherwise noted, spaces containing tokens are still considered to be empty for the purposes of these effects.

So yes, a monster can expand into/sit on a Search token if it wants to. As Mustard says, the heroes can still Search that token even with a monster on top of it. The only condition for the Search action is that they must be on OR adjacent to the token.

Mustard said:

I think you could "greedy" a search token 3 spaces through a monster because those are still countable adjacent spaces.

Correct. FFG has confirmed that "within X spaces" abilities do not require line of sight unless they say so, and Greedy does not say so. (In fact I believe Greedy was the ability that prompted the question in the first place.)

Note that such abilities DO depend on the ability to "count spaces" though, and counting spaces through a door or wall doesn't work as those things break adjacency.

Thanks for your help!