Why does my lexer throw an unexpected char exception in the middle of my comment or string rule containing a wildcard?

Most likely you need a charVocabulary option to specify the set of characters you expect. The wildcard or ~ operator make no sense unless you bound the set of possible characters. For example,

SL_COMMENT
options {
        paraphrase="SL_COMMENT";
}
        : "//" (~'
')* '
'
                { $setType(Token.SKIP()); newline(); }
        ;

charVocabulary = '3'..'377';