Bitwise operations may be your best choice. There are no 24-, 6-, or 26-bit types in unpack's formats, and vec demands its chunks be a power of two bits wide and aligned. Here is one way to do it, unpacking to three ints and doing the bit operations.

$fh->read(my $buf, 12);
my ($var1, $var2, @raw) = unpack 's s L2' $buf;
my ($var3,$var4) = map { ($_ >> 8, $_ & 0xff) } $raw[0];
my ($var5,$var6) = map { ($_ >> 26, $_ & 0x3fffffff) } $raw[1];
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That's not quite as unportable as it looks, but it's still on the edge.

Update: Differs from Stevie-O's by bit order of the C struct. I'm not sure which is correct, so I'd bet on his. Adjust to what works :-)