The actual myth of Osiris had no real connection to the life of Jesus, although I have seen silly claims that Osiris ‘resurrected’ and so on - easily discarded by simply reading the actual Book of the Dead, which is available online for free.
Mithras is different. The original cult had no connection, or almost none, to the cult that grew up about one hundred years after the death of Jesus. However, older religious cults were greatly reverenced by the Romans, while new ones were regarded as tainted or dubious in some way, so someone swiped the name and started the Mithras cult that became so favored by Roman soldiers.
It’s this cult that was a favorite of Roman soldiers that you sometimes hear people talk about in connection with Jesus. Most of the claims are utterly bogus.
As with most of the later mystery religions we have little information about their actual beliefs. The reason they were called mystery religions was because their tenets were only told to those who paid their way into the cult. The more you paid, the more you learned, and the greater your status in the cult. This may not have had much to do with actual cult worship, and certainly not with belief - you could buy your way into a group of fellow citizens, feast with them, and perhaps they would help your business or status in some way.
Of course, this was the opposite of Christianity, since Christians were eager to speak to anyone, any time, about the beliefs of Christianity.
Because we have no books written by the cult members today, we have to rely on what other people who lived at the time wrote about them.
Mithras was a favorite of the Roman soldiers, and apparently, you could pay money, or have bull’s blood splashed over you, or attend one of the sacrificial feasts, and this would guarantee you wouldn’t die in the next few battles. You can see why it was favored by the Roman soldiers.
The sacrificial feasts, just as all other pagan sacrificial feasts, ‘fed’ the god or god statue in some way, again, the opposite of Christianity, but since you paid your way in, the god would favor you for feeding him. Pagan religion was much like Roman society, strongly patron/client.
As for the many confusing tales told online about Mithras (complete nonsense, such as a virgin birth or claim of salvation for believers, an especially silly claim, since no pagan religion has anything to do with what we think of as faith) I suggest you read ‘A Separate God’ by Petrement.