I find it hard to weigh the relative bogosity of the claim that "for the love of Mike" refers to some particular Edmonton bookmaker and the claim that it's over 600 years old. Both ideas seem quite unlikely (to put it politely) to me.

The suggestion of a link between Pete and "for pity's sake" is a good one. I wish I'd thought of that.

To say " for Christ's sake" was frowned upon a while back, so I think it's not unreasonable to think that "Pete" and "Mike" became euphisims for it. I believe the Irish said "For the love of Jaisus", which is a softer way of saying "for Christ's Sake". The Irish have a way of saying harsh things softly. Minds me of the American South. You can say "your Baby is really ugly, Bless his heart" and get away with it. Sometimes it's not the statement but how one says it. ---And it makes me shudder that 75% of people now say "for f**K's sake.

#14 -- It isn't. And you can't say "Your baby is really ugly, bless his heart" and get away with in the US South. (If by "get away with it" you mean something like "keep the good opinion of the person your talking to." If you mean "not get shot," then it depends.)

On second thought, it does seem to me that the Irish may reserve "for Christ's sake" or "for the love of Christ" for occasions requiring stronger oaths, and use "for the love of Jesus" a little more freely. Actual Irish please correct. There's no good reason for that that I can think of and I wouldn't use either one in the presence of a priest (whose good opinion I wanted to keep).
No second thoughts about the ugly baby, though.

Yes, jaysus is just how the English spell what they think of as the Irish pronunciation of Jesus. But no, "bloody" does not come from "by Our Lady." That's an old myth that never seems to die.
I am under 40- still quite a few years off, and use "bloody", and I've heard others my age and younger use it. It's kind of a substitute for what we would normally say though and mostly used in front of parents, grandparents etc as they won't be offended by it. Since I work with a lot of Americans I use "bloody" since it seems to amuse them.
Reading letters written years ago with old-fashioned slang is always interesting- I was reading letters written by my then-17-year-old grandfather to my grandmother which he wrote from a NZ navy ship in the Pacific near the end of the war. He used the words "gee" and "swell" all through the letters- seems so cute now, but was probably a cool way to speak/ write then.