I’m hoping you already know about the “cloud” settings in Notepad++, but just in case you don’t:
Go into Settings -> Preferences -> Cloud -> and select the Set your cloud location path here: radio button.
Then enter the DropBox folder path into the text box below it. Note that you’ll need to have your DropBox mapped to a local folder, not the internet URL. (See Note 1 below.)
When you restart Notepad++, it will copy certain files from %APPDATA%\Roaming\Notepad++ folder to your DropBox folder.
Having established how to move settings to the cloud, I’ll make a disclaimer. Setting up cloud settings in Notepad++ is the only thing I have experience in. I have not tested the suggestions below, and I’m not a Notepad++ developer, so my suggestions below are merely from using the software and reading the forums for many years. But here are my suggestions on plugins and sessions.
Regarding sessions, perhaps the best way to share those across computers is to use the Load Session… and Save Session… options on the File menu. That does require that you save and load each session manually as you leave and start using each computer, but that’s not necessarily a bad thing, and may avoid some problems with trying to share sessions more automatically.
The sessions are managed by use of a session.xml file. Presumably, you could sync the %AppData%\Roaming\Notepad++\ folder to DropBox for each computer (see this post for a way to do that via symbolic links), but this is where I know it gets tricky. The session.xml file is read on startup of Notepad++, and it only saves the primary session (if you have multi-instance mode enabled). So if you have session.xml on a shared, softlinked folder, and primary sessions open on two different computers, presumably, when file settings are changed on computer A, they will not change on computer B until Notepad++ is (possibly closed, then re-) opened again. So if you were diligent about closing all sessions of Notepad++ before switching computers, it probably would work ok.
If it causes problems, you may need to use the Load/Save Session options or otherwise manually sync the session.xml file while Notepad++ is closed. Also see the section on sub-folders below.
For plugins, you should be able to install the plugins you use on each computer used - a one-time setup for each computer. (See Note 2 below.) But I’m guessing your main concern is the settings of the plugins. Those settings appear to be kept in a folder in %APPDATA%\Roaming\Notepad++\plugins\config, which won’t be a problem if you are able to successfully redirect the Notepad++ folder. If not, presumably, you could sync that folder to DropBox in a similar way, possibly with fewer side effects than syncing the whole Notepad++ folder.
There are two sub-folders in the %AppData%\Roaming\Notepad++\ folder: plugins and cloud. The plugins folder is discussed above. However, the cloud folder should contain a file named choice (no extension) after changing the cloud settings in Notepad++, that holds the local path to the DropBox/backup folder. That means that if you share the Notepad++ folder with session.xml and the cloud folder, each computer must have the same path to the DropBox folder (or a softlink to it, I guess). So if the DropBox folder is C:\Users\dsavant\DropBox\npp on one computer and C:\Users\dmsavant\DropBox\npp on another computer, it may be difficult to get this to work, especially if you don’t have rights to create users on both boxes.
So I think that’s all I can tell you about sharing settings, plugins, and sessions across the internet. Perhaps a Notepad++ developer will chime in with clarifications. A couple of parenthetical notes, though:
Note 1: I do not have a DropBox account, although I do have OneDrive and Google Drive accounts. For each of these, there is software to install that maps a local folder (a sort of symbolic link, I believe) to the filestore in the cloud. I assume DropBox has the same type of software/mechanism available.
Note 2: The plugin DLLs appear to be kept in the Program Files folder. One would need to test to see if simply copying the files from that folder on one computer to that folder on another computer would result in functioning plugins, but I would imagine actually installing them on each computer shouldn’t be much of a hardship (a one-time activity per computer), unless you’re truly installing and uninstalling plugins on a regular basis. The configuration files seem to be the part that is more likely to change.
Good luck on getting these to sync, and post back if you get it working or if you run into problems!