This is definitely a challenging age! My only real tricks are distraction when I am trying to get C dressed or change his diaper. I keep a couple cars/trucks that are new and exciting near where I change him and I try to sort of keep them away from him for the other parts of the day, but only let him play with them when I need him to lay down. He also loves books, so I try to keep some interesting books nearby for those times, too. It doesn't always work. And, honestly, if it doesn't work, I just hold him down and change him. Too much going on these days to sit around and try to figure out how to convince him to do something. And, if he throws a tantrum, I just get what I need to done, and then I lay him on the carpet and let him do his thing and I walk away. Thankfully C's tantrums are much shorter than my 3 year old's. C is just a less challenging child than N, but I can't remember if N's tantrums at this age were this short or not. As he got older N's got longer and more terrible, so I may just not remember what he was like at 20 months! : ) Everyone keeps telling me that 4 year olds are easier. I certainly hope so!!!
ETA: I just saw your question about whether these were the terrible 2's.... unfortunately, at least from the experience I am having with DS1, the terrible 2's were easier than the terrible 3's. My 3 year old is WAAAYYY smarter and it is constant testing all.day.long. But, he is a REALLY strong willed kid, so I am hoping it is not the same with DS2, who is a much easier going kid. I think it differs for each individual child, somewhat dependent on their dispositions. I am really praying DS3 tends towards DS2's disposition or I don't know what I will do!!