In the first attack, a roadside bomb killed two US soldiers on patrol in the Khogyani district of Nangahar, a US military spokesman said on Tuesday.
Another roadside bomb killed two Afghan soldiers and wounded four others in eastern Kunar province, said General Zahir Wardak, a commander in the region.
Separately three people were killed and eight wounded when explosives being fixed to a motorcycle blew up in a religious school in Ghazni in southeast Afghanistan, a senior provincial official said.
The head of the school and the the bomber were arrested on suspicion of planning attacks.
A teenage suicide bomber also blew himself up next to a combat patrol north of Camp Salerno, the US-led coalition's main base in Khost, a small mountainous province bordering Pakistan's tribal region of North Waziristan.
"The suicide attacker was a teenager. He was wearing new clothes, which is the sign he was dressed for the grave," said Rahmat Shah, a villager who witnessed the attack.
The latest attacks come during the bloodiest period in an insurgency that has been raging since US-backed forces ousted the Taliban government from power in 2001.
Defence ministers from the Nato are due to meet in Brussels on Thursday to give a final blessing to plans to virtually double Nato peacekeepers troop strength from 9,000 to 17,000, giving the US scope to wind down its forces.
However, the number of US troops will remain at around 20,000, Ronald E Neumann, US ambassador in Afghanistan, told journalists in Kabul this week.