Chennai:
Okay so from what I gather your one son was turned 10 around Nov. and your other 7 around September. In Alberta your child must be a certain age by the end of February. So your eldest will be in Grade 5 and your youngest in Grade 2.
There are some private schools in Calgary but not worth it. There are two public (government systems) in Calgary. One is the Catholic system for those who are baptized Catholic as it surrounds a lot of the teachings around the religion. The other is Calgary Public which is for everyone else (ie. Jewish, lutherian, muslim). Both are good systems. I can't recommend a school as your school is designated by the area you live in. English is the primary language at the schools, however there are some that are strictly French. Otherwise French is a second language at most of the schools and some provide Spanish. You will find that some have more technology than others.... unfortunately that's what happens in a big city. Don't expect that because they are government schools that its free.... you do have to pay your school fees each year and buy school supplies. As for extracurricular in the elementaries (Kindergarten to grade 6) not much is offered. More is at the Jr. High (Grade 7-9) and High school (10-12). However, there are things offerred in the city that your kids can join (soccer which is the europe football, hockey, swimming, karate, etc). I would suggest that if you are going over before the rest of the family you contact the school boards directly (both have websites) and find out how the registration process works when you are coming over from another country.
As for your wife... qualifications may differ from India to Canada so if she is wanting to teach at the universities or colleges she should again contact them directly or search their websites for job opportunities. There maybe some things that she would need to upgrade in. Same if she were to teach in one of the schools.