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Opus Dei is all about integrating God into your daily life – with regards to mortification, most of the guys seem to keep it private and hidden, where it belongs. As St. Josemaria Escriva said, we should "choose mortification that don't mortify others." I'm paraphrasing a bit, but there's a specific section of "The Way" where he talks about someone who fought every single day not to put sugar in his coffee – he called these sorts of battles heroic. That's what mortification is at its heart – denial of the self for the love of God. It's abstaining from one good to choose a higher one.
Now, with regards to the cilice, flagellation, hairshirt etc – these are advanced mortifications for those advanced in the spiritual life (and for those who are already practicing the "simpler" mortification – denial of food, hot showers, etc). I don't do any of those things because I am pretty far down as is. Moving too soon to the harsher mortification can lead to you to do them out of a damnable spiritual pride – with each lash you'll just be bringing yourself closer to Hell and farther away from God. That's why it's so important to get a good spiritual director who can analyze these things and figure out what's best for you. One of Opus Dei's main services is spiritual direction, so definitely go find an Opus Dei priest and explain your situation. It's possible you are ready for these things but looking at things just probabalistically, it's highly unlikely.
"Joining" Opus Dei depends on how you plan to do it. There are three "levels" so to speak – Cooperators, Super-Numeraries and Numeraries. Anyone who assists "The Work" is a Cooperator – this means praying, almsgiving, etc. For those who wish to go further, you can become a Numerary, a celibate male or female who gives his or herself fully to The Work. They live in the Opus Dei centers and go to work "normal" jobs in most cases – judges, lawyers, business men etc. Supernumeraries are similar except they can get married and do not live in the Opus Dei centers.
Right now I am just a Cooperator, but I will become a Supernumerary soon after my wife and I get married. I might be mistaken on a couple things but I am 90% positive this is an accurate picture of Opus Dei. If you're really curious though definitely try to find an Opus Dei center in your area – they are super friendly and will be thrilled to show you around and explain everything to you.
Let me know if I can help with anything else.