(Not a teacher)
No, because most people don't even agree which day comes first - Sunday, or Monday. I guess if you decided that Monday was the first day of the week, you could make them odd and even, but it isn't an established thing and if you said to someone, "I'm going to the gym every even day of the week", they wouldn't know whether it was Monday, Wednesday, and Friday (Sunday the first day of the week); or Tuesday, Thursday, and Saturday (Monday the first day of the week).
There are odd and even days insofar as dates are concerned - Today is an odd day because it's the 11th.