Integrated IR receiver is more than capable handling most if not any IR remote. All you need is correct keymap. Chances are that there is already working keymap that just need enabling. Note, I'm far from being expert in this field, so I can't give you any better explanation that it's already on wiki.
Of course it's possible to wake up or power on board via IR. However, protocol and key number must be selected at build time (limitation of power management firmware.) Due to that fact, default protocol and button on boards which come without remote (including OrangePi 3 LTS) is RC9 MCE power button. This combination was selected due to popularity of windows media center remotes. If you want to customize this, you have to build your own image with adjusted configuration. But good news is that usual LE updates don't update U-Boot, which, among others, contains power management firmware and is responsible for loading it. So you have to do this only once.
Any power button, be it on board or on IR remote, only brings up power menu in Kodi. I'm not aware of any direct way to power it down or sleep with one press.
Note, other power up options are power button on board and HDMI CEC (although CEC might not work reliably - still under development.)