A.P.
My oldest weaned himself also and was not found of cups, sippy cups or bottles. I found that he really enjoyed straws. I found some "water bottles" with a built in straw and we did that for ages. If the rest of the family picks up using straw cups too he might be more inclined.
Also, if he is refusing milk and formula it might be more than just resisting. It could be he is allergic to milk and is trying to tell you. He doesn't have to break into hives to be allergic. My oldest was the same way and we found his irregular bowels after breastfeeding was done was due to this issue. Try soy or rice milk and see if he takes to it instead. Sometimes after breast feeding the milk can seem thick too. My son liked it mixed about 1/3 water to 2/3 milk when I did get him to drink it before we found out he was allergic.