The bombs, apparently in stationary cars, struck the Shola neighbourhood after dark on Wednesday, causing widespread damage and casualties on the district's main street, near a restaurant and close to a car repair workshop, police sources said.
A fourth explosion struck the Palestine Street neighbourhood of central Baghdad, apparently targeting a convoy of vehicles from the Interior Ministry. It is not known whether there were casualties.
The two months since a Shia-led government was formed have been accompanied by a series of attacks by fighters.
US soldiers killed
Meanwhile, three US soldiers were killed by small arms fire during combat operations west of Baghdad, the military announced on Wednesday.
The soldiers were killed on Tuesday near the city of Ramadi, 115km west of Baghdad, the military said.
They were attached to the US Army's 2nd Brigade Combat Team, which is assigned to the II Marine Expeditionary Force.
More than 1700 members of the US military have died since the beginning of the Iraq war in March 2003.
Iraqi security forces, meanwhile, detained 30 people for staging attacks, Aljazeera reported.
A leader of the Turkmen Front also escaped a bid on his life in central Kirkuk when a car bomb exploded. Aljazeera said two of his guards were wounded in the attack.