I have 4 pieces of walnut, a bit over 1/8" thick, and about 5" wide and
18" long.

What is the best way of edge gluing these together?

I have tried clamping, (and taping) but can not see how to keep all the
pieces level with each other. To make matters worse, the pieces are
perhaps +- 1/16" of each other in thickness. I don't have a drum sander,
so was hoping to glue them so one face is in a plane, and to sand/scrape
the other face smooth.

Any ideas?

Thanks,
Harvey