iD tech 4, under cost you have put unknown. It is now open sourced under the GPL and freely available. I don't know if GPL allows you to sell products based off of it but in the case of iD tech 4 the data files that it loads (which basically constitute your game) can be sold commercially for no license fee, you own those.
Irrlicht you mentioned being open source under cost, but many of the other projects there you did not mention being open sourced such as Ogre-3d
Source you can commercially sell mods for, of course you then need the NDA if you wish to distribute engine aswell or rely on the end user having another steam game already installed.
Updated, to represent all free versions that are also open source.
As to idTech, it is open source, but it is not free for use. If you want to ship a commercial product with it (AKA, you want to make money), you need a commercial license. In prior versions, they charged about 10 grand for such a license ( a few games were published this way ). But under Zenimax ownership, I have no details.
In regards to source, the entry was for licensing the engine, as opposed to modding it. Modding any of the engines is a completely different license, generally a non-commercial one without written permission otherwise.
Thanks for the feedback.