"I don't know about serger. Does it cut the fabric off and stitch back and forth over the edge?"
yeah, it sure does.
if look'n for strong, i'd go with sewing.
not sure if you can do a for-real flat felled seam at home on sil, but you can get awful close, except you're going to still see a raw edge. at any rate, you can split the load over two lines of stiching.. sort of.
one can, if desired, pull the knife down and disable it, then you can have a wrapped edge, and plus maybe even a three thread cover stich. i can not see this being as strong (or easy), as a couple of lines of std stiching. but at least you won;t have cut off an edge and thence be hoping it;s just threads holdiing it all together.