If its not necessary to use reshape
out <- unlist(lapply(SV37.refined, as.character))
out[out != "0"]
## Sample11 Sample21 Sample22 Sample181
## "string1" "string2" "string1" "string3"
or if you're into one-liners
Filter(function(x) x != "0", unlist(lapply(SV37.refined, as.character)))
## Sample11 Sample21 Sample22 Sample181
## "string1" "string2" "string1" "string3"