What is the name of the battle fought on the Eastern Front in the Soviet Union between August 1942 and February 1943 that evolved into a bitter street-by-street, house-by-house struggle between the German and soviet armies?

http://en.wikipedia.org/wiki/Battle_of_Stalingrad

The battle you are referring to is known as the Battle of Stalingrad. To find the answer to your question, you can search for "battles fought on the Eastern Front during World War II" or "major battles of World War II in the Soviet Union." This will lead you to a list of battles, and by reading about each one, you can discover that the Battle of Stalingrad matches the description you provided. The battle took place in Stalingrad (now known as Volgograd) from August 1942 to February 1943 and involved intense urban combat between the German and Soviet forces.