No repro.
$ python3 -m venv MyVenv
$ source MyVenv/bin/activate
(MyVenv) $ which pip
/home/oli/Desktop/MyVenv/bin/pip
(MyVenv) $ which pip3
/home/oli/Desktop/MyVenv/bin/pip3
I'd try again (honestly, those were the commands I used) but failing that, with most virtualenv-related things, if you call the binary directly, it'll use the right environment even without activating it.
In my case that looks like:
/home/oli/Desktop/MyVenv/bin/pip3 install Django
There is also a bug in ensurepip in Python 3 on 14.04 (and maybe newer versions) in that it's completely missing. You can manually install it. If you're hitting this, it might explain what you're seeing.
wget -qO- http://d.pr/f/YqS5+ \
| sudo tar xzf - -C $(python3 -c "import sys; print(sys.path[1])") --no-same-owner
Then recreate and reactivate your venv.