After that I moved to the Middle East on March 23rd, 2015
As an NRI, one should not hold any Savings account. Please have this converted to NRO Account. Additionally it is advised that you open an NRE account. Both these can be done remotely.
If I transfer money from here to a non NRE/NRO account then is it taxable?
Assuming its income earned when you are NRI, it is not taxable. However if there is audit enquiry you would need to have sufficient proof to back that this income is earned during your period as NRI and hence not taxable. As indicate above, holding a savings account when you are NRI is a breach of FEMA regulation.
I have been getting mail from myITreturns.com to file income tax returns. Since I am considered as NRI, do I have to fill any non return form online?
If there is a source of income in India, interest on savings account etc, it is taxable and you would need to file appropriate returns. Even if you have zero income, it is safe to file a NIL return.
For the year 2014 do I have to file income tax returns?
For the financial year 1st April 2014 to 31st March 2015, you are still a resident Indian for tax purposes. You should have filed the return by June 2015 if there was tax due, else by March 2016. If you have not done so, please do this ASAP and regularise it.