I understand that a Sol is a Martian day, a little longer than a day on Earth (... 30 minutes I think?) and there are 24 months using the Darian calendar. So if people lived on Mars, what is a casual way of keeping time on it?
An answer to your question depends strongly on whether those Martians were colonists from Earth and retained close ties or not and to what extent they spent time on the surface of Mars.
If they did not retain close ties, then their timekeeping would be based mostly on the Martian day and Martian year. (They'd still use the Earth-derived second because changing that would be such a pain for technology, and there's no real reason to change it.)
Assuming that they interacted with the Martian outside -- like working outside or living under transparent domes -- they'd probably want to synch their day to the sol. The Martian year would also probably be important to them (though they would keep on tracking Earth years also), but weeks and months would be no more connected to anything Martian than they are connected to anything terrestrial here on Earth.
My guess is that they'd have the Earth second, Earth minutes and hours (simple multiples of seconds), and a "Martian time slip" added during the night to make up the sol. They would almost certainly keep a week of seven sols just out of habit. Months could go either way: twelve longer months, 24 months about the same length as ours or something else. Unless they went through some sort of revolution where they deliberately cut themselves off from earth, they'd certainly also keep track of things such as ages in Earth-years, since there's so much cultural stuff in Earth years: Terrible Twos, Sweet Sixteen, Three score and ten, Centenarian, etc.
If they lived underground and hardly saw the surface, they'd probably stick with Earth time and have an app to tell them what the Martian day and season is.
If they remained part of a unified culture with Earth, they'd endlessly juggle things: They'd use Earth time, and the sol for the day, and probably use seven sols for the week, but longer periods would probably be Earth-based recording Earth years and maybe even Earth dates for anything official. There'd be apps for that!
And bright kids would become endlessly fascinated with all the lovely complexity. (While adults would curse it, and murder mysteries would be solved by Syaloch pointing out that the miscreant confused an Earth date with the similar Martian date.)
Use a clock that is set for local time. As soon as Mars was colonised these would be developed as a matter of course. Could program one myself without too much effort on my computer, and I'm not a developer.