I've used getc to read the byte stream and vec to test the first and second bits of the byte. Depending on the result of the tests I either just unpack an unsigned char or append one or two more getc() operations, mask off the first two bits and then either unpack() a network short (2 byte piece) or a left-padded with 8 0-bits network long (3 byte piece). I have not incorporated error checking for incomplete reads.

use strict;
use warnings;

use 5.010;

my $mask2  = pack q{CC},  0b00111111, 0b11111111;
my $mask3  = pack q{CCC}, 0b00111111, 0b11111111, 0b11111111;

my @packed = (
   pack( q{C},   0b01010101 ),
   pack( q{CC},  0b10101010, 0b10101010 ),
   pack( q{CCC}, 0b11001100, 0b11001100, 0b11001100 ),
   );

my $byteStream = ( join q{}, @packed ) x 3;
open my $byteStreamFH, q{<}, \ $byteStream or die $!;

while ( defined( my $piece = getc( $byteStreamFH ) ) )
{
    unless ( vec $piece, 7, 1 )
    {
        # 1 byte piece
        #
        say unpack q{C}, $piece;
    }
    elsif ( vec $piece, 6, 1 )
    {
        # 3 byte piece
        #
        $piece .= getc( $byteStreamFH ) for 1 .. 2;
        $piece &= $mask3;
        say unpack q{N}, pack( q{C}, 0 ) . $piece;
    }
    else
    {
        # 2 byte piece
        #
        $piece .= getc( $byteStreamFH );
        $piece &= $mask2;
        say unpack q{n}, $piece;
    }
}

close $byteStreamFH or die $!;
[download]

The output

85
10922
838860
85
10922
838860
85
10922
838860
[download]

I don't know how quick this would be on a large volume of data but I would imagine that a solution in C would be somewhat faster.

I hope this is of interest.