First, install tox into your virtualenv:
pip install --upgrade tox
To run all tests, you'll need to install multiple Python interpreters. On a
modern Ubuntu distribution you can use add-apt-repository
ppa:deadsnakes/ppa.
Depending on if you can install the wheels directly for your OS, you may need the libraries to build PIL, too. Here's the Ubuntu commands:
sudo apt-get install build-essential python-dev python3-dev sudo apt-get install libjpeg8-dev zlib1g-dev
Finally, just run tox!
If you want, you can test against a specific version like this: tox -e py36