Roddick engineered a turnaround to triumph 4-6, 6-3, 6-3 over world number four Nadal, who was the highest seed left in the draw.
Berdych, who saved a match point en route to a stunning upset of world number one Roger Federer in the fourth round, dismantled Söderling 6-2, 6-2.
Berdych, who said he wanted to be "aggressive but with lots of control" was able to do just that. He broke Söderling four times and faced only one break point himself.
Berdych reached the second prestigious Masters 1000 final of his career, after winning the Paris title in 2005.
Now he has a chance to become the first Miami men's champion not ranked in the top 10 since Jim Courier in 1991.
"It is nice to take a match like that. I was playing really well, not too long on the court," Berdych said.