Overhang climbs are ones that are angled at more than 90 degrees (like angled or vertical roofs). They often seem intimidating to the uninitiated, but there are some neat techniques that make this process much easier. There are also some myths surrounding the strength needed to climb overhangs. Having upper body strength is important, but more significant is a person's core strength, as well as her ability to use her legs as much as her arms.
Focus on Footwork
Solid, exact footwork will be immensely helpful because it can help take the weight off a climber's arms. Toe cams (when you jam your toe in a crack and or hole in the rock), toe grabs (when you hook a hold with your toe), heal hooks, and even something as simple as pressing a foot on a hold can help a climber engage her core or leg muscles.
Drop Knee Technique
Try the drop knee technique. To do this (on the right side), grab a good hold with your left hand at or below shoulder height, and pull it toward you. Your arm should be as straight as possible because that position is engaging the fewest muscles and therefore is not as tiring. Then bend your knee, turn your right hip in, and tuck it as closely to the wall as possible. This will allow you to reach up higher with your right hand to snag a hold that is just out of reach. It will also alleviate some of the weight that is on your arms because you will be utilizing different muscles, such as your biceps, rather than hanging straight down on your shoulders (which is more tiring). Though strange feeling at first, you can save energy by "drop kneeing" your way up a steep climb.
Hanging With Straight Arms
As you climb a steep wall, it is better to not constantly engage your biceps by staying in a bent-armed position. Instead, when you get to a decent hold, try straightening your arms and hanging. However, make sure to also engage your shoulder and back muscles when you are hanging with straight arms so as to alleviate the stress on your tendons.