All games on Sora Stream support keyboard and mouse to play. As for playing with a controller, Sora Stream supports controllers with XInput, as for example the Xbox controller, although final compatibility will depend on whether the game has support for playing from a controller. See here for a list of recommended compatible controllers.
If you access Sora Stream from your mobile phone, you can use your remote controller via Bluetooth. In case you don't have one, Sora Stream will add touch buttons on the screen to make your experience easier.