1) Do they have a right in the said property? (I assume they can claim a share in the 33% of my mom's aunt but I had read somewhere about tenancy in common and joint tenancy, please clarify)
Yes your mother's aunt is entitled to an equal share to that of you and your mother in the property purchased jointly on all the three persons name. No question of common or joint tenancy, the legal heirs of the deceased shareholder can always stake their claim for their respective share in the property.
2) All the people mentioned above have agreed to sell the property and divide the proceeds EXCEPT the youngest son of my mother's aunt to prevent the sale. The society is therefore refusing to grant NOC for sale. We have tried contacting him but to no avail. We have put a public notice in the newspapers regarding the same. As he continues to ignore, what is the legal procedure to sell the flat without his NOC?
A share holder if not willing to sell his share in the property, the others can approach court for partition of the property and once the court finds it that partition is not possible in the dwelling house, on the basis of advocate commissioner's report, it may be brought to public auction and all share hlders will get their money according to their proportion.
3) Can the society refuse NOC for lease. Do I need NOC of any of the heirs of the deceased for lease ?
Yes, if the society is refusing to give NOC for lease, it is mandatory to obtain NOC from other share hlders for the same.
4) Can we (I and my mom) sell off our 66% share. If yes how ? Please advise any way to get rid of the property and getting our share knowing that one of the sons isn't responding at all.
You and your mom can sell your undivided share in the property to the purchaser who is willing to buy it, here is no legal infirmity in it.