Moon Knight is the avatar of the Egyptian god Khonshu. He mostly is a regular (strong, agile, good fighter, ex-mercenary) person with a truncheon and some crescent shaped darts. He has a mystical side though in that things seem to work out for him and when he is down Khonshu seems to come through for his path to victory. His strength also rises and falls with the phases of the moon (I think this is only in later incarnations of the charcater). He has beaten a werewolf, characters with superhuman strength, Tigra, a lot of street punks, etc.. He has three identitites and uses them to keep his ear to the street. He can use his cloak to glide a bit. That's about all I can think of for now.
During a Spider-Man issue Moon Knight and Spidey were searching Hobgoblin II a.k.a. Jason P. Macendale, that was hired from the Foreigner to kill Nick Katzenberg, fighting with Spidey, Macendale throwed some pumpkin bombs and the building, old and ruined, proceed into collapsing.Meanwhile Moon Knight was taking safe the abitants of the building, Hobby gained the upper hand on Spidey, Katzenberg saved him, and Macendale shooted him with an electrical blast, Spidey beat down him, then leaved the building with Hobgoblin and Nick, they were able to get out cause Moon Knight was substaining the main door of the building and with it the ENTIRE WEIGHT of the main wall of the building.
But during that period his strenght was fluctuating, I don't know if he's still that strong.