Electrical – Can power outlets and HDMI wall-jacks be installed with right-angle bends to accommodate very thin walls

Since this is the accepted answer, I can't delete it. But after another decade of DIY work, I agree with the comments below. This is not code, and not safe. Device power cables are not intended to be run in walls and are a fire hazard. IMO, @gregmac's answer below is correct, provided you use proper electrical cables in the wall (as gregmac notes in the comments).

@Jeremy has a good solution, but if you're willing to do a little more work, there is a little better-looking answer. Since you're running an HDMI cable, I assume you have some kind of small stand/table in front of the outlet that your cable box sits in or on.

With a drywall knife, punch out a hole behind the TV and install a plastic "old-work" 1-gang box. Don't worry, we're not going to install electrics here; just a plastic box that has a couple of "ears" on it so it can slide into existing drywall. Do the same thing at the bottom of the wall, above your electrical outlet. You can now run the cables easily through the wall without patching any drywall. If everything's laid out correctly, both will be hidden (one by the TV, one by the stand/table that holds your cable box).

To help you with the terms, what you're looking at from above is the top plate. Frequently there are two 2x4's for a top plate. Two boards are used for added structure at the joints and extra fire proofing. This gives you about 3" of wood to drill through.

As ChrisF mentions, you should run a stud finder up and down the wall cavity near the halfway point to see if any fire blocking has been installed. This would be a single 2x4, and will almost always be in a wall if the ceilings are over 8' tall.

You'll significantly reduce the odds of insulation in the wall if you are doing this project on interior walls. You should also be avoiding any electrical in the same wall cavity (between the same two studs). You would see an outlet, switch, or wire coming out of the top plate if this were the case.

As for the actual wiring, I've used these low voltage mounting brackets for the hole in the wall. Place the bracket on the wall where you want the opening, mark the corners and sides, and cut out the drywall with a drywall saw. Test fit the bracket and file back any spots that are blocking you until you get a snug fit. Then bend the tabs back into the wall and tighten them with a pair of pliers. On that bracket, I use a modular plate (these comes with more openings if you need them) and then an ethernet jack mounted in the plate. You can also get jacks for cable, phone, stereo, etc.