They said the attacks in the western province between 10 pm and midnight local time on Tuesday also wounded a total of 26 police.
Violence in Iraq has reached a level not seen since 2008 and militants, including those linked to al Qaeda, frequently target Iraqi security forces and other government employees.
Four of the attacks struck targets in and around the town of Rutba, about 110 kilometres from the border with war-racked Syria.
A suicide bomber detonated a tanker truck loaded with explosives at a police checkpoint east of the town, while militants armed with heavy weapons struck the police station in Rutba itself and another bomber detonated a vehicle at a police checkpoint to its west.
Those attacks killed 18 police and wounded 25, while three civilians died when another suicide bomber blew up a tanker truck on a bridge west of Rutba.
At about 11 pm on Tuesday, gunmen attacked a police checkpoint at an entrance to Ramadi, the capital of Anbar province, killing three police and wounding a fourth, the sources said.
Gunmen also hit another checkpoint in the city, killing four more police.
The violence was just the latest in a series of coordinated attacks to hit Anbar province.
On Monday, a suicide bomber detonated explosives at the entrance of the police headquarters in Fallujah, another city in Anbar, while a second struck the nearby electricity department headquarters.
Militants then hit the police headquarters from three sides with gunfire, mortar rounds and rocket-propelled grenades, entered the electricity department building, and fired on police with sniper rifles.
The violence killed two police, including a major, and wounded four others.
Interior ministry spokesman Brigadier General Saad Maan, meanwhile, said the security forces killed five suicide bombers in Fallujah, and that two police were wounded.
And on Sunday, suicide bombers attacked government buildings in Rawa, a town north of Fallujah that is also in Anbar province.
Two suicide bombers on foot and another driving a vehicle rigged with explosives attacked the local police headquarters in Rawa, while another bomber in a vehicle struck an army checkpoint at the town's entrance.
Another three bombers on foot and a fourth in a vehicle attacked the local administrative headquarters while officials were meeting inside.
The bombings killed at least eight people, including three members of the local council for the area and three police.
With the latest attacks, more than 520 people have been killed so far this month, and more than 5,200 since the beginning of the year, according to AFP figures based on security and medical sources.
A study released this month by academics based in the United States, Canada and Iraq said nearly half a million people have died from war-related causes in Iraq since the US-led invasion of 2003.
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HMMMM, wasn't everything supposed to be peaceful in IRAQ after the Americans left, (some years ago now)??? Lessons for Pakistani wishful thinkers after 2014!!!