When you like something , you have a pleasant feeling/regard for it/ feel good about it. When you enjoy something , you get pleasure doing it and get a sense of satisfaction. I like playing all sports , but soccer is the game that I most enjoy playing. Did you enjoy your meal?=Did you have satisfaction/pleasure from your meal ? Did you like your meal?= Did you think the meal is good? I enjoy playing football > you get pleasure/satisfaction from playing this game. I like playing football > you feel good when playing football. They are quite the same, but "enjoy" gives you a stronger sense of satisfaction/pleasure. Its like "feel good" versus " satisfaction"

Well, you would generally enjoy a verb, but like a noun (or you could like a verb too) 'I enjoy playing football' works. 'I like football' works Even 'I like playing football' works. But 'I enjoy football' isn't totally wrong. But you would not really hear it.