What are common climbing techniques for strongly overhanging walls and roofs?
In order to avoid a strength oriented climbing style and focus on technique.
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Here are a couple
Overhanging climbing is hard work and tiring. You need to reduce the stress on your muscles by letting your skeleton hold as much of your body weight as possible. Keep your arms straight and your muscles relaxed, don't try and hold yourself against the face. Pull only when you need to pull
When reaching on overhanging terrain in order to make better use of your skeleton (above), if you twist your body (for example) to the left with your (for example) right hand straight, your left hand will be able to reach further without you pulling with your right bicep. This allows you make tough moves with the lowest amount of effort.
Unless you're Adam Ondra, you're going to get more tired on overhanging terrain. Try and keep moving. If you have to keep stopping to work out moves, etc. you're going to run out of energy. Visualise the moves, etc. before you start. This will save energy when you get to the moves as you won't have to try and figure them out when you get to them, all the time wasting energy.
Foot work is even more important on overhanging terrain.
Don't let your feet fall behind your hands. If you're too stretched out you will swing away from the wall and you'll have to pull hard to get back on it. You want your knees bent most of the time.
You can't expect your hands to hold your entire body weight for an extended period of time. You need your feet to hold as much of your weight as possible. To do this you need to tense your core. This requires core strength(stomach/back) which may take some time to build. You also may need to use techniques such as heel hooks. The idea being that your feet are working to actively hold you against the wall rather than simply being along for the ride!
The best single tip I got when I started bouldering (especially overhangs) is
use the backstep
I don't know if that is the official name. It's what we called it.
It's intuitive but it's incredibly effective to give you more reach.
For supporting yourself on left foot and right hand: