The 11 former trainees claim they were abused at St Peter Claver College, run by the Verona Fathers, in the 1960s and 70s.
It is alleged that one boy was as young as 11 when he was abused.
In total, the order, now called the Comboni Missionaries, has paid out £120,000.
Most of the men have waived their right to anonymity and say they spoke out to force the order to acknowledge what went on.
They claim they were abused during fake medical examinations, when they were told to 'purify' their bodies.
It is also alleged that one priest scraped a cross into a boy's chest using his fingernail, saying pain "brings you closer to God".
The majority of the 11 say they have experienced mental health problems because of the alleged abuse.
In a statement, the order said it felt "deep sorrow" for anyone who was hurt.
It added: "All the claims were made on a purely commercial basis and with no admission of liability.
"Considering the number of boys who were educated at St Peter's, the Verona Fathers absolutely do not accept that claims from 12 individuals demonstrate a culture of abuse at the seminary."