The two policemen were killed in a drive-by shooting while shopping, and died instantly. The soldier was killed near a city hospital, police said of the incidents which occurred on Tueday.
The attacks, about 60km northeast of Baghdad, came as vote counting continued in Iraq after elections on Sunday.
Counting has been completed for five of 18 governorates, a spokesman for the independent electoral commission said in Baghdad. The commission was waiting for the results from a number of the 5000 polling stations across Iraq, he added.
The votes are being checked and registered into a database in the election control centre adjoining the residence of the interim prime minister inside the capital's fortified Green Zone.
The count would still take a few days as 65,000 lists of results had to be accounted, said the United Nations chief electoral adviser to Iraq, Carlos Velenzuela.
Meanwhile, leading Sunni clerics declared any government emerging from Iraq's election would lack legitimacy because many people had boycotted a poll they said was tainted by US-led occupation.
"These elections lack legitimacy because a large segment of different sects, parties and currents ... boycotted," Iraq's influential Association of Muslim Scholars (AMS) said.
"This means the coming national assembly and government that will emerge will not possess the legitimacy to enable them to draft the constitution or sign security or economic agreements."
"All Iraqi people are waiting for the opportunity to hold comprehensive, free and just elections that have legitimacy and write the constitution it wants after the withdrawal of the occupation," the AMS said.
The influential group said it would respect the wishes of the voters but that the any new government's powers would be restricted.