I have a quest where the player has to go to certain parts of the Wasteland, use a radio there, and return to his terminal.
To this I created a new ingestible item named Radio.

How would I make it work so activating the radio triggers next stage of the quest? I obviously need condition GetDistance and stuff, but where would I apply this script? Right into the item with OnActivate Player script or somehow into the "Results" section?
Also, how can I make sure that the item remains in player inventory when it's activated?

The injestible item can have it's own script assigned to it. I believe you would use an 'ON Equip' block to run the commands to advance the quest - SetStage, etc. Your main quest script can check to make sure one of these items is always in the Player's inventory after it is consumed.

You could try making your effect script somthing like:

if QuestStage == 2
set QuestStage to 3
else
showmessage RadioHasBeenUsed
endif
player.additem radio 1 1
end

The syntax maynot be 100% right but that would be the basic idea.