"Perl newbie here, ..."

Start by reading "perlintro: Perl introduction for beginners".

"... and I am faced with the following problem: ..."

As already pointed out, PerlMonks is not a code writing service. See also: "How (Not) To Ask A Question: Do Your Own Work".

This was an interesting little problem, so I coded a solution that produced your "desired output". Here's the pseudocode for my solution:

ALGORITHM: find_common
    INPUT: list of files (file_list)
    DECLARE: hash of IDs (id_hash)
    CALL: get_data WITH references to file_list and id_hash
    CALL: get_common WITH reference to id_hash

FUNCTION: get_data
    INPUT: file_list and id_hash
    LOOP: file_list EACH file
        OPEN: file
        LOOP: read line EACH line
            remove line terminator
            split line INTO id and string
            LOOP: split string EACH substring
                increment id_hash-id-substring value
        CLOSE: file
    RETURN: void

FUNCTION: get_common
    INPUT: id_hash
    LOOP: id_hash EACH id
        LOOP: id_hash-id EACH substring
            SKIP: id_hash-id-substring value < 2
            PRINT: id : id_hash-id-substring key
    RETURN: void
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If you make an attempt at implementing that in Perl, I'll gladly review your effort and show you mine. There would be many ways you could code this; but do note that there is nothing complicated in the logic — if you read perlintro, you should have all of the tools necessary for this task.