What you have described sounds like you might only use 5 of the embroidered blocks, one in the center and one on each side???
Anyway, 20" is a very odd size for an unfinished block. You have to allow 1/4" on all sides for the seam, so you would be looking for a block that finishes at 19.5", which basically doesn't exist. You can't use four 10 inch blocks, because that would finish at 20.5 and not fit with your embroidered blocks.
What I would do is look for a 12" block that you like. Here's a selection from quilter's cache:
http://www.quilterscache.com/BlocksbySizeC.html
Make 4 of these and join them, resulting in a big block that would measure 24.5" square. Add a fabric 'frame' to your embroidered blocks, either white to blend or a contrasting solid to really frame it, to bring your embroidered squares up to 24.5". Now all the blocks will fit.