The idea was to put the specific parts in the case statement and then have a general-purpose piece of code just like you had already at the end, except it uses whatever was defined in the case statement above. But okay, here you are.

Code:

untgz () {
  gunzip -c <"$1" | tar xf -
}

for l in "$@"; do  # invoke this on a bunch of named files
  case $l in 
    *.tar.gz) ext=".tar.gz"; command=untgz;;
    *.tgz) ext=".tgz"; command=untgz;;
    *.tar.Z) ext=".tar.Z"; command=untgz;;
    *.zip) ext=".zip"; command=unzip;;
    *.ZIP) ext=".ZIP"; command=unzip;;
    *) echo "$0: cannot handle $l, skipping" >&2
        continue ;;
  esac

  A=`basename "$l" "$ext"`
  mkdir "$A"
  cd "$A"
  $command "$1"
  cd ..
done

The function is required for tar.gz because we want a command which takes exactly one parameter as its last argument, so we have to rearrange things a bit and create a function which does that. For most formats you will simply need to add a command= which already works as specified (archive name is sole argument to command), so you don't need a separate function for it (witness unzip).

The extension handling is kind of ugly; with associative arrays that would be easy to put into a table, but the shell doesn't have that facility. You could still think about ways to make it a bit less atrocious. Maybe a while loop which reads extensions and commands?

Code:

  # ... code as above, this replaces just the case statement
  ext=
  while read x cmd; do
    case $l in "$x") ext=$x; command=$cmd; break;;
  done <<____HERE
    .zip  unzip
    .ZIP  unzip
    .tar.gz  untgz
    .tar.Z   untgz
    .tgz  untgz
____HERE

  case $ext in '') echo "$0: dunno how to handle $l -- skipping" >&2 ; continue;; esac
  # ... continue as before with A=basename etc

Next you will tell us this was a homework assignment and your lecturer didn't understand how "your" code works, and gave you an F. Oh well.

Actually, your code looks good as well, you just need to put the mkdir etc before the case and the cd .. after the case, but then you will need to figure out a new way to extract just the base name of the archive. It's generally a good idea to put all related information in one place, thus I wanted the case statement to contain all the stuff which is specific to each file type.