Here is a little run-down of the possible situation with a short explanation.
Controllers have 2 ways to communicate:
- Xinput, the modern protocol. Almost all modern games (especially the XBOX 360 ports) will work with these controllers. They usually have "soft" trigger buttons, meaning they replicate the action of real life triggers. Also, similar to XBOX 360 controllers, they have a Home button. Usually in the front, between start and select. These controllers use analogue input for some buttons, meaning the buttons (mostly the triggers) read data in more precise float point values (e.g.: 0.165 and 0.734).
- DirectInput, the older protocol. Older games use this and some modern games (fighting games always support these, Assassin's Creed 2 & BroHood etc). Think of PS2 era controllers. They have regular button triggers and usually no home button. Games working with the Xinput as their primary input mode usually won't support these controllers. The triggers are using digital input, meaning they have less precise values being sent (1 pressed and 0 unpressed). (Even Steam's Big Picture supports this mode, but you won't have access to the steam-in game overlay and screenshot functionality, because you'll be missing a Home button with this)
After you determine what type of controller you have, you need to see what type of controller your game supports.
Modern games support almost all the time the Xinput method, especially if the game was ported from consoles to PC. They rarely support DirectInput.
The Elecom controller seems to be DirectInput (the big MODE button is not a Home button and the triggers are buttons). It won't get detected by most modern games. Luckily for you, there is a piece of software called x360ce made to emulate Xinput for DirectInput devices. I see that you have used it with no success.
Download the latest release from here, their official homepage of the project: http://code.google.com/p/x360ce/ and follow the instructions they provide on their site here: http://code.google.com/p/x360ce/wiki/Whatisx360ceandhowuseIt
Following that guide properly should make your Elecom controller work.
The XBOX 360 controller should have no issue working with Batman: Arkham Origins, BUT the official drivers should be installed on the system. I found that just plugging it in isn't enough. Download them from the official Microsoft driver repository here: http://www.microsoft.com/hardware/en-us/d/xbox-360-controller-for-windows
Keep in mind, when you want to use your XBOX 360 controller in a Xinput only game, unplug the other DirectInput controllers. Games have a tendency to ignore the XBOX 360 controller if they detect a DirectInput controller. I think it has to do with the priority the system is setting to each one of them (actually this happened to me when I was playing Arkham Asylum, and I had to unplug my Logitech Wireless Rumblepad 2 and restart the game).
The same thing applies when you install the XBOX 360 controller, remove all other controllers. Once you install it, reboot and plug in the others keeping in mind the above mentioned.
Hope this will help.