If you use the bobblehead stand or magazine racks do I assume correctly that they still work for you? [duplicate]
Solution 1:
Picking up a SPECIAL Bobblehead gives you a stat increase, just as if you'd picked it yourself as a Perk. This happens as soon as you pick it up. There's an added benefit that if you're already at 10 in that SPECIAL, the Bobblehead will push you to 11.
Picking up any other Bobblehead grants a special perk, but it doesn't show up anywhere you can see it.
Each of the magazines grants a special Perk that show up in the list in your PipBoy. Some stack (e.g. Barbarian), while others do not (like Astoundingly Awesome).
In either case, once you've picked up the magazine or Bobblehead, the actual object is completely useless. Put them on display, dump them in a river, fire them from a Junkjet (maybe?). In any case, the actual object no longer matters.
Solution 2:
Yes, you continue to have the stats even if you sell the items :)