My gosh, that poor guy is in really rough shape! Since you are new to reptiles, and have just 'inherited' him, I'm really surprised I'm the first to respond to these photos.
The bearded dragon is suffering from a serious medical condition with a mouthful of a name, "secondary nutritional hyperparathyroidism". In short, he is severely deficient in calcium, and has been for a long time--long enough for his jaw bones and other bones to become weak and deformed. He is also slightly thinner and darker than I would want to see a bearded dragon.
Can you give us details on his caging and setup? Calcium deficiency can be caused by lack of calcium in the diet, and/or lack of
UVB light and vitamin D3. Bearded dragons MUST have a strong UVB reptile light, at the appropriate distance from them for basking. They must have high heat, and all insect prey should be dusted in a quality calcium powder. Use of a calcium powder containing vitamin D3 once or twice a week is also recommended.
Poor diet and lack of UVB are the usual cause for this problem. It's vitally important that the conditions and the diet be corrected immediately, to prevent further damage, and allow his bones to strengthen. His jaw will never look normal again. This condition doesn't happen over night, it's caused by inappropriate diet or lighting over a long period of time.
You definitely don't need to worry about this dragon becoming overweight at this point--he could still stand to put on many more grams before he'll be up to a typical weight for his size, and some of that may be edema from the hypocalcemia. Be sure that the greens you choose are nutritious, and don't contain excessive oxalates. Turnip tops, dandelion greens and flowers, and mustard greens are all good choices. (Avoid lettuces, cabbages, broccoli, etc). Feed greens every day, and a light dusting of calcium wouldn't hurt, given his condition. Insects can be fed every other day, as many as he will eat in 15 minutes.
As most will agree, you should make an appointment with an experienced reptile veterinarian, to get him a checkup. The vet may recommend additional supplements, and can check for other health problems that may be present.