Auto extracting software for Linux?

You could maybe try a little mini-daemon along the lines of:

#!/bin/bash

DOWNLOAD_DIR=~/Downloads

while true;
do
    for file in $DOWNLOAD_DIR/*.tar*;
    do
        if [ -f $file ]
        then
            tar xf $file
            if [ $? -eq 0 ] # remove if successfully extracted
            then rm $file
            fi
        fi
    done
    sleep 5
done

Just start that running and away you go. I'm not sure what the performance implications of a bash forever loop would be, but just looking at it in top it doesn't seem to be too bad (i.e. it isn't in there.) You could boost the sleep time if necessary.