Try:
ls -1 | grep -E "\.tar\.gz$" | xargs -n 1 tar xvfz
Then Try:
ls -1 | grep -E "\.tar\.gz$" | xargs -n 1 rm
This will untar all .tar.gz files in the current directory and then delete all the .tar.gz files. If you want an explanation, the "|" takes the stdout of the command before it, and uses that as the stdin of the command after it. Use "man command" w/o the quotes to figure out what those commands and arguments do. Or, you can research online.