As others have said, the first pair are conditions and the second pair are bitwise operations, and you can learn all about them in perlop. For a little more illustration, I'll show Perl that does the same thing without the operators you're asking about.

Conditions:

if ( ! $v ) { $v = $w }    # $v ||= $w;
if (   $x ) { $x = $y }    # $x &&= $y;
[download]

Bitwise operations:

$v = $v | $w;              # $v |= $w
$x = $x & $y;              # $x &= $y
[download]