One of the men suspected of terrorist activities by the Ethiopians told Swedish public radio that they were sometimes taken to a room to be whipped.
"They would try to strangle us, saying: 'today you will tell the truth. If you don't tell the truth we will cut you to pieces'. They strangled me until I passed out," he said.
The man says that he showed his injuries to staff from the Swedish embassy.
"Yes, I showed my hands. I think there was also something on my throat that I showed," he said.
In addition to the ambassador and other embassy staff, the men also received visits from a foreign ministry official and the Swedish Security Service, none of whom reported any signs of torture.
The three were helped in their return last week by the Swedish embassy in Addis Abeba.
The three Swedish citizens were taken prisoner at the beginning of the year. A fourth prisoner, a pregnant 17-year-old, was released in March.
The group were arrested in Kenya, having fled Somalia after the invasion by Ethiopian troops which brought about an Islamist retreat. Around 60 others were also arrested and sent to Ethiopia via Somalia.
The prisoners were accused of fighting on the side of the Islamist militia against Somali government forces and their Ethiopian allies.
Human rights organizations criticized Ethiopia for holding the prisoners in contravention of international law.
Earlier in the month, Sweden had demanded the immediate release of the three. The foreign ministry summoned Ethiopia's ambassador in order to hand over a formal protest.
At first Ethiopia rejected the demands, saying that "the suspects of terror, whatever their nationality, should be brought to the court of justice".
Sweden's foreign ministry was not been given an explanation for the about-turn, and nor was it clear if the suspicions against the Swedes remain.
"I have no information about the details of the release. All along, we've demanded that they [the Ethiopian authorities] either give us an explanation of the legal grounds for the arrests or let them go free," said Cecilia Julin.
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