There was a discussion recently on RugTalk (an online group for people interested in weaving rugs), about sewing rag strips together with a serger to prepare them for weaving. Although I have two sergers, I haven't used this method myself for rugs. My reasons for not using the serger are that I think I can do it just as quickly with my regular sewing machine, the serger uses more thread, and the seam isn't as stable as one made with a sewing machine.
The main positive reason I can think of for using the serger is that it saves some time trimming the little triangle away from the seam, since the serger does it while sewing the seam.
Don't think that because the serger has a cutter, it should be used to cut your fabric strips. It isn't a very fast method, and will quickly wear out the two blades on the serger, and eventually wear out the motor.
Here are some tips to use a 3/4 thread serger. First of all, I would use the 4 thread (two needle) stitch to sew the strips together. The 3-thread stitch pulls apart too easily.
Clip the strips apart.