Comment: Early Christians probably borrowed elements from the cults of Mithras and Osiris when they were developing their new Jesus religion, but it's also possible that the similarities between these three savior gods simply reflect a common strain of religious ideas that had been in circulation in the ancient Mediterranean world for millennia.
Mithras and Osiris are much older than Jesus. The first mention of Osiris dates back to Egypt's Fifth Dynasty (~2494 to 2345 BC) and Mithras was "an ancient Indo-Iranian god adopted in the Roman empire as the principle deity of a mystery cult which flourished in the 2nd and 3rd centuries AD," according to the Oxford Classical Dictionary (OCD), 3rd ed. revised.
The Osiris cult spread through the Roman empire after the Roman conquest of Egypt. Mithraism, popular with the legions, was introduced after the Roman conquests in the East. Christianity, an obviously syncretic religion with many pagan elements, evolved from a combination of Egyptian, Roman, Asiatic and Hellenized Jewish influences. In many cases, the early Christian church simply appropriated pagan ideas and festivals as part of its ongoing culture war against paganism.
Mithraism has many similarities to other religions of the time. The beliefs of the cult have to be pieced together from inscriptions and artwork, however. According to the OCD, "the cult is known primarily from its archaeological remains. Over 400 find-spots are recorded, many of them excavated meeting-places. These and the ... dedicatory inscriptions give a good idea of cult life and membership."
In the case of Christianity, it's hard to know whether the beliefs of the Jesus cult simply emerged through a process of syncretism or whether the Christians just stole their ideas from the pagan belief systems they were competing against. Both of these things probably happened at the same time. One way or another, the "new" religion was hardly original and it could have lost the culture war to Mithraism if it hadn't acquired enough secular power to suppress its competitors.