What's the best way to get a 20-month-old to take an afternoon nap?
When children start to walk or make other major transitions, all of their behavior, including sleep, gets reorganized. My best guess is that you're going through one of these transition periods. You'll have to shift as well. You can't make him sleep more, but you can adjust his sleep distribution across 24 hours. It sounds as if he does need some daytime sleep, which most children do at this age.
Start by moving his nighttime bedtime later by about half an hour. In a week move it later again by the same amount. Wake him up in the morning at his usual wake time. Keep him from napping in the morning, although he may want an earlier lunch. Keep the afternoon nap ritual very simple. Even if he doesn't sleep, be sure he gets at least an hour's quiet time with books and one stuffed animal; it'll turn into a nap eventually. Don't put him in pajamas or do some of the other things you do at night, as he may not really be ready for the big separation that nighttime sleep involves. And it may be that big separation of night that he's fighting. Don't let him sleep more than one to one and a half hours in the afternoon or you may find nighttime sleep reduced.
Once you've taken these steps, back off. The more this turns into a fight, the more he'll resist.