Can an overstayed visa alien marry a permanent resident and apply for a green card while in US?

You can get married, but from an Immigration standpoint, it will not grant you legal status. If you are overstayed, you must leave the country and return LEGALLY in order to appropriately take advantage of the US laws and constitution. You can also apply for a green card, however, it will not be granted because your are not eligible being overstayed with an expired I94. You are an ILLEGAL alien, thus you loose your privileges.