I don't know about the Japanese question, but certainly there would have been numerous battles between the Bf110 and the P38.

I will have a look and see if there is any info on the general outcome of these battles. But the two planes are ostensibly a fighter (P38) and a Fighter/Bomber (Bf110). So, in a dogfight situation I certainly would rather be in the P38. In my opinion, a far superior 'interceptor' and 'pursuit' aircraft. Although the Germans did use the 110 as an 'escort'.

Both American and British pilots flew P38's as frontline fighters in Europe and Nth Africa, at times, so there should be at least some info around.

I'll check. 

  I got this idea of twin engine fighters facing off against each other and couldn't get it out of my mind, so much so that I even went out and bought some referance material on P-38s.
  It seems that P-38s came up against Ki-45s several times, from New Guinea, to the Philippines and even in China.  In one encounter a P-38 came face to face with a Ki-45.  The Ki-45 pilot, intent on attacking the B-24s the P-38 was escorting, didn't see the P-38 coming at him.  The P-38 pilot, wanting to avoid the heavy firepower of the 'Nick's nose armament, dove down to a lower altitude, slid under the Ki-45 then came around and shot the 'Nick' down from the rear quarter.
  Even more numerous were the encounters between P-38s and not only Me-110s, but Me-210s and Me-410s also!  These battles took place over North Africa, Italy and Europe.