Old Japanese Wii games on US Wii U

Unfortunately. the Wii U is region locked(this means Virtual Wii as well). This means it can only use software printed for its home region. USA and Japan have different region codes, so they cannot use eachothers software, only their own.

To make matters worse there is currently no way of bypassing the region lock without just importing the region's console (the region code is hardwired into the hardware).

Mostly Nintendo is the only company that still region Locks. Xbox One is completely region free as is the Ps4.

Source

Yes, unoffically though (it may break you warranty).

Region locks can be bypassed without modifying the Wii/virtual Wii, by loading homebrew software through certain game discs (like Super Smash Bros. Brawl or Lego Batman). And in addition to that you can install a small unofficial (and safe) channel called 'The Homebrew Channel', which allows you to run unsigned applications without inserting a specific game disc every time that was used for the initial exploit used to install the channel.

This will guide you through the process: http://wiibrew.org/wiki/Homebrew_setup (this site is updated quite often).

You can then use either Gecko OS, or the smaller but newer WiiLauncher, run through the channel, to load game discs region free (I recommend you put both on your SD Card, incase one throws an error).

There is also a piece of homebrew that changes your Wii's region, but modifying you Wii in a large way is not recommended, as Nintendo could break it with an update, and large modifications are not completely understood.