How can I secure a power extension socket on the wall without nails? Answered

They make Pop in Boxes for this. Cut hole to size of box and it's secured with pressure from the tab in the Pop in box.

I like Zengineer's idea of making a stand of some sort for it -- ether wedged in place, or just resting on a suitably stable foot -- if you really don't want to touch the wall (eg, if your landlord's an obnoxious type).

Otherwise, I second Lemonie. Unless you're dealing with wallpaper, it shouldn't be hard to patch and paint the holes when you move out. They shouldn't have to be larger than the holes you'd use when hanging a picture or (perhaps more to the point) putting up a shelf.

The 3M releasable tape is good stuff, but you need to think about just how much weight you're going to want this to carry. Too much weight over too small an area, and either the tape or the face of the wall may  let go even if the tape doesn't.

Use nails / screws. Any secure method of attaching the thing to the wall will leave more of a mark. Yes you'll have a couple of holes, but that's not the same as patches of tape-residue or ripped-off finish.

L

If you really don't want to mess up a wall ,perhaps you can wedge a 2x4
between the ceiling and the floor,and keep it close to the wall.
Then  just mount the extension on the 2x4.
Somebody probably makes some kind of expandable rod that would wedge between ceiling and floor too, most likely for shelving, but off hand I don't know who......

3M makes a type of double-sided tape that can be easily removed.  It's often bundled in pre-cut strips with a matching hook, but you can buy them separately, too.

Screws!