Say I have a creature with Adventure in my graveyard, for example Murderous Rider, and something allowing me to cast creatures from my graveyard (for example Liliana, Untouched by Death ).
Am I allowed to cast the adventure part of the card from my graveyard?
What if I’m allowed to cast instant and sorceries instead of creatures?
Maddening Imp does destroy creatures that enter after its ability has resolved.
The main relevant rule is rule 611.2c:
If a continuous effect generated by the resolution of a spell or ability modifies the characteristics or changes the controller of any objects, the set of objects it affects is determined when that continuous effect begins. After that point, the set won’t change. (Note that this works differently than a continuous effect from a static ability.) A continuous effect generated by the resolution of a spell or ability that doesn’t modify the characteristics or change the controller of any objects modifies the rules of the game, so it can affect objects that weren’t affected when that continuous effect began. If a single continuous effect has parts that modify the characteristics or changes the controller of any objects and other parts that don’t, the set of objects each part applies to is determined independently.
The first part of Maddening Imp’s ability is a continuous effect that does not change any objects’ characteristics or controller, so it can affect objects that weren’t affected when the ability resolved. The delayed triggered ability is then not associated with any particular set of creatures when it is created, so it determines the set of creatures to destroy as it resolves in the end step.
This is confirmed by the rulings in this Reddit thread.