GNU tar supports the -z and -j flags, which allows extraction of compressed files without a pipeline:
tar -xvzf archivefile.tar.gz
tar -xvjf archivefile.tar.bz2
Inside the DSM-G600 you can't use those flags, so there you must use a pipeline:
gunzip -c archivefile.tar.gz | /mnt/HD_a2/tar -xvf -
/mnt/HD_a2/bzip2 -dc archivefile.tar.bz2 | /mnt/HD_a2/tar -xvf -
[bzip2 can be obtained here. It's a bzip2 archive, so you'll obviously want to extract it before you install it onto the DSM-G600 .]
In windows you can use various applications to extract tar.bz2 files: