I'm not entirely sure I understand your question, but I think what you are looking for is:
script.sh "$some_multiline_string" "$another_multiline_string" param1 param2
Then, inside the script, you would have:
file1="$1"
file2="$2"
param1="$3"
param2="$4"
If you really need to pipe it, you could do something like this:
printf '%s\0%s' "$str1" "$str2" | script.sh param1 param2
And, in the script:
#!/bin/bash
param1="$1"
param2="$2"
strings=()
while IFS= read -d '' str; do
strings+=("$str")
done
printf 'String 1: %s\n\nString 2: %s\n' "${strings[0]}" "${strings[1]}"
For example:
$ str1="this is
a multiline
string"
$ str2="this is
another multiline
string"
$ printf '%s\0%s\0' "$str1" "$str2" | foo.sh
String 1: this is
a multiline
string
String 2: this is
another multiline
string
In bash versions 4.4+, you can do:
#!/bin/bash
param1="$1"
param2="$2"
strings=()
readarray -t -d '' strings
printf 'String 1: %s\n\nString 2: %s\n' "${strings[0]}" "${strings[1]}"