What happend to the troops from August 1944 to May 1945. I know thatthe Polish troops and I believe the Indian (Kurkha's ) were there.
Yes, they were there with the British 8th Army. My explanation, above, was trying to stay focused on the American units and specifically the 5th Army. The Polish corps and the 10th British Corps was placed under the command of the US 5th Army during the early battles of Cassino. Afterwards, they were moved back to the 8th Army command.
The II Polish Corps was on the left wing of the British 8th Army at the Spring 1945 Offensive. They were the unit to the right of the 5th Army's right wing and they pushed up through Imola, cut Highway 9 and moved in to help take Bologna. Most books say the Poles liberated Bologna, but that was just so they could have some publicity. As you know, the US 34th RED BULLS reached Bologna first. 
Steve