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Not a Historian, but just a useful (sort of) bit of info: Such words have a name, they're called minced oaths.
I know Latin very well. It's difficult to talk about swear words in Latin because basically all of our preserved texts were written by upper class Romans who did not reproduce spoken, colloquial Latin. Rather, they primarily use a heightened formal literary style. For excited utterances, like "dammit" or "ugh" Romans usually use the name of a god. The most popular were "mehercule" or "hercule" which is "by Hercules!" or "Iove", "by Jove" or "dii magni" "by the great gods!" in the same way Shakespeare uses "zounds" referring to "Jesus' wounds" or "sblood" or "Jesus' blood". I suppose those are "g" swears. From graffiti in Pompeii, which is one of the only places where we can see colloquial Latin, and in poets like Catullus and Martial, we know of a lot of nasty names to call someone, but you get the picture.
I don't see many replies, so I'd recommend asking on /r/linguistics.
They also have a Q&A thread that updates weekly you can ask in.
Follow up question: When did such words become a thing?
Not to discourage constructive participation here, but you might consider crossposting to /r/latin, where the community will be primarily, well, Latinists.
As /u/jbizzel points out, many (not all) of our Latin sources don't lend themselves terribly well to informal language. Latin certainly has its vulgarities, as found in Catullus and Martial, but it's often difficult to decide precisely how crude an obviously crude term is meant to be, especially if it is only used once or a handful of times. I offer the famous example of the verb glubit, which Catullus uses to describe his ex-lover's actions "at crossroads and in alleyways." The background meaning of the word appears to mean to "peel the bark from a tree" -- Catullus gives us little to know what precisely this means, except that it is certainly an insult, so interpretations have ranged from the mild (to rob, as in "to fleece" in English) to the rather intensely vulgar (to peel back the foreskin -- even that is exactly as vulgar as you let your imagination makes it). So, if we found ourselves in ancient Rome and decided to show our street-smarts by throwing that word out in a witty conversation, would we get chuckles or shocked expressions in return? It's very hard to tell.
Again, as /u/jbizzel says, a large number of Latin curses are divine invocations, and may have had varying levels of intensity, but it does appear that mehercule (occasionally shortened to mehercle) was quite mild, and I also offer that there's a fun pair of ecastor (a mild swear used only by women) and edepol (used only by men), which references the famous Gemini, Castor and Pollux. I'm not certain it's ever been explained to me properly why men get Pollux and not Castor, whether that be simple luck or because Pollux was the originally divine twin.
From Plautus and Terence we know of at least three,
mecastor!, or ecastor!, ("by Castor!") an interjection used by men.
medepol!, or edepol!, ("by Pollux!") similar, used by women.
mehercle!, ("by Hercules!") similar to ecastor, used also by women in rare (and possibly erroneously recorded) cases.
Mehercule etc. have already been mentioned, so I'll pass those over. The closest thing I can think of is the idiom "flocci non facio," which English translators typically render as "I don't give a hoot." It's hard to literally translate, but more or less literally means, "I don't make it one straw in value." Unfortunately, it's hard to tell whether this would've been considered a mild oath, or whether it was just an idiom.