The Tu-22M3's nose houses a Leninets PN-AD radar and a NK-45 navigation and attack system. The NK-45 provides improved low-altitude flight, compared to earlier models.
Several Tu-22M3's were converted to Tu-22M3R who carry a Shompol side looking airborne radar and other Electronic signals intelligence equipment.
All this equipement is stored in the nose of the aircraft. This explains the strange appearance (The asymmetry between the top and bottom).
I can only guess why the nose is asymmetric: Maybe some parts of the equipment located in the nose has to lock forward / down of the plane. The asymmetric bottom may provide a better "view" for the equipment. (See my comment below).
On this image, you can see all the equipment in the nose. Unfortunately the quality is too poor to be able to read the caption.
The Tu-22M had a retractable probe on the top for aerial refueling:
As a result of the salt negotations, the probe was removed but it could be reinstalled.
because with refueling it was considered an intercontinental range strategic bomber.
the Soviets secretly agreed to reduce Tu-22M production to thirty aircraft per year and not to give them an intercontinental range.
Stratetic Arms Limitation Talks 2