The answer to your question depends entirely on the mods in question.
With some mods, taking the appropriate .txt or scene files and placing them in the folder of the other mod will do the trick.
For slightly more complex mods one must combine the .txt code of the two mods using a merger/differencing tool to help find the different lines of code.
For most major mods (mods that do more than add a few items, or troops, or improve graphics) one must actually merge the source code that is eventually compiled into the .txt files that run the game.
So, depending on what you are trying to combine, your answer will vary greatly. In most cases, you should be able to get a sense of which of the above three will work within the mod's thread/board. Almost always there are instructions for how to use a given mod with others, or how to install it properly, etc; some mods post their source code. But there is no generic response to your question.
For 1866 and Invasion, this will most likely require the combination of the source code--the Module System files for each mod. I do not know if they are "open source" in that they have their source posted. .txt 'splicing' would be difficult and may cause unseen errors. For the specific case you've listed, it may not be possible.