Hi, I'm Dr Steve. My first thought is that his Temperomandibular joint is out of place, but that wouldn't allow him to eat very well. The fact that you can close it manually without pain makes a totally dislocated TMJ joint less likely. This could be related to a nerve problem in the masseter ( cheek ) muscles which control opening and closing the jaw. If he has a neuropathy he may have these symptoms without pain. This condition is not very common, but it can happen and can be caused by inflammation in the nerve.
Another possibility is that for some reason he is choosing to keep his mouth open. THis may be due to some issue inside his mouth that may be causing discomfort when he closes the jaw. The only way to determine which of these possibilities is going on would be to have him examined by a vet who will thoroughly examine the inside of his mouth and who can also do some tests to see if the nerve seems to be affected or not. If it is a nerve problem he may need steroids and with nerve damage, the sooner the condition is treated, then better the results. SOo the best thing to do would be to have him examined and preferably today to get the best response. You can mention these possibilities when you take him to the vet. Things that could be going on inside his mouth could be an infected tooth, an ulcer on his cheek ( inside) or gums , or tartar buildup /gingivitis ( infected gums) . I hope this has helped. If it has would you please click the submit button so i may receive credit for my answer. I will check later today to see if you have more questions. THanks for using just answer and good luck.