Assuming a simple, comma-delimited file where every comma is a delimiter (some csv files may have quoted commas that ought not to be treated as field seperators), the following prints every line except the header when a column in the header is "SOMESTRING":
awk -F, ' FNR==1 { for (i=1; i<=NF; i++) if ($i == "SOMESTRING") next nextfile } 1' file1 file2 file3 file4
The string comparison can be replaced with a substring test or a regular expression match operation, if appropriate.
nextfile is not part of POSIX AWK, but it is widespread; it is available in at least gawk, nawk (used on *BSD systems), mawk, and busybox.