I have 4 sets of wires (light and 3 outlets, all are black and white, no ground) coming into a box that holds the light switch and one of the outlets. I want to replace the outlet with a GFCI. How do I wire this?

Twist all grounds together and tuck in the back of the box.
Twist all whites together, with an additional short wire(pigtail), This connects to the GFI's Line side Neutral.
Determine which wire is your hot/feed, and twist together with 2 black pigtails, 1 goes to the GFI line side hot, the other will go to the switch, then twist all remaining blacks together(lights) and add a small black pigtail which will connect to the switch. Also ground the GFI. Another pigtail from your grounds.

Twist all grounds together and tuck in the back of the box.
Twist all whites together, with an additional short wire(pigtail), This connects to the GFI's Line side Neutral.
Determine which wire is your hot/feed, and twist together with 2 black pigtails, 1 goes to the GFI line side hot, the other will go to the switch, then twist all remaining blacks together(lights) and add a small black pigtail which will connect to the switch. Also ground the GFI. another pigtail from your grounds.

Couple of more questions, I don't have any ground wires, do I just ground the GFCI to the metal box? Also, the three remaining blacks, one will be for the light switch, the other two will be for the other outlets, can I twist the ones for the other outlets together with the hot wire?

Anything you want live all the time, like the outlets, connect to them, You could even add another pigtail that is constantly hot and switch a second set of lights, or half or a receptacle, if you break the tab on the hot side of the receptacle to separate halfs, The small slot(dark screws.