Here’s variation on trippledubs’ solution using the 3-dot form of the flip-flop operator:

#! perl
use strict;
use warnings;

my $re = qr{^//\*+$};

while (<DATA>)
{
    if (my $seq = /$re/ ... /$re/)
    {
        if ($seq > 1 && $seq !~ /E0$/)
        {
            print if m{^//\s*\S+};
        }
    }
}

__DATA__
// useless comment

Some Code

//**********************************************************
//
//I need that text
//   And that also
//
//**********************************************************

Some Code

// useless comment

//**********************************************************
// More text
//**********************************************************

More code
[download]

Update: Changed print unless m{^//$}; to print if m{^//\s*\S+}; to filter-out non-comment lines.

Output:

 1:25 >perl 1128_SoPW.pl
//I need that text
//   And that also
// More text

 1:25 >
[download]

Hope that helps,