In addition to the South East Asia theatre, Indian divisions were involved in the North African and Italian campaigns. By the end of the war the Indian Army was over 2 million men strong.

There was also the Royal Indian Navy and the Indian Air Force- both of these were relatively small and mostly involved in the Burma and Malaya campaigns though some Indian ships went to the mediterranean, and individual Indian airmen served in UK based squadrons of the RAF.

I would think that the empire would have used some of our population as soldiers

You are absolutely correct. The British saw India as a valuable source of manpower, and well over a million Indian (referring to the Raj as a whole) soldiers served in both World Wars. In WWII, the British Indian Army saw combat in Europe, North Africa, and the Asia-Pacific. As /u/ParkSungJun mentions, Indian forces played a vital role in the Burma Campaign (given the geographic proximity of Burma in relation to the Subcontinent). The Indian 4th Infantry Division (which still exists today) fought in the Sudan, Syria, North Africa, and Italy. In total, around 87,000 Indian servicemen died in the war.

Many Indian divisions were deployed by the British in the Pacific, including Malaya/Singapore, Burma, and during the battle of Imphal/Kohima in Manipur, India. You may be interested to know that Subhas Chandra Bose, one of the advocates for Indian independence, helped organize a "Indian National Army" under Japanese supervision which took a good amount of the Indian prisoners from the surrender of Singapore. Also fascinating is the inclusion of an all woman regiment, the Rani of Jhansi regiment, named after Lakshmibai, the Rani of Jhansi who fought against the British during the Sepoy Mutiny.

After the war, the Indian National Army was repatriated to India, and several of its officers faced trial for treason. The ensuing anger by the Indian population ended up causing enough unrest against the British Raj, eventually leading to their 1949 withdrawal from India.

It was the largest volunteer army in recorded history, with over 2 million signing up and almost 1.5 million seeing active service. I am amazed this isn't taught in Pakistani school history lessons. It's an integral part of the story of British withdrawal from India as well as being pretty major in World History generally.

http://www.bbc.co.uk/history/ww2peopleswar/timeline/factfiles/nonflash/a6651218.shtml

Mr Ghandi of the Indian National congress was opposed and wanted Britain to surrender to Germany. Mr Jinnah of the Muslim League (a quite important guy in the founding of Pakistan) was very concerned about India's future if the Allies lost and supported the war efforts.

Although the population of India (meaning the 'Raj' including Pakistan, Bangladesh etc.) was overwhelming Hindu, a very high proportion of volunteers were Muslim or Sikh. Much higher than their relative demographic strength.

http://defencejournal.com/sept99/martial-races.htm

There were also Indian volunteers in the Nazi Wehrmacht, but much, much smaller numbers http://www.feldgrau.com/azadhind.html