Disabling the firewalls will solve most issues with joining/hosting games for Warframe.
Here's how to do it:
1. In the run command (windows key+r), type in wf.msc

2. Click on Windows Firewall Properties
3. Select "off" for "Firewall State" in Domain, Public, and Private Profiles

4. Restart your computer.

Note: The "Strict NAT detected" error might still show up but you will now be able to join and host games.

This is pretty much what I did and although the error still pops up and I don't see some of my friends online, we can still play by manually selecting the mission we want at the same time. I can even host and join games through online matchmaking.