First of all both of you should have one or the other identity cards. Otherwise marriage certificate cannot be issued. Go to that Chennai temple, Meet the Manager or Purohit and get a signed certificate for having held the marriage on such and such a date.
Next you can prepare an affidavit through the help of an Advocate declaring all the details required by the Marriage Officer. Three witnesses are absolutely necessary. They will be arranged by the office on the sport. U have to pay something to the witnesses.
Before scratching your head, go to the nearest Sub Registrar's office and get all the details. Everything stands on bribe now a day. Carry sufficient money in your pocket. Start bribing them, the work will be done within no time.
But I do not believe that your wife has lost all the documents. Here u r telling a bland lie. Women are very careful than men in such matters. At least what happened to her school certificates like SSLC certificate, Transfer Certificate, Cumulative record issued by the school to prove she is of proper age.
Boy should be above 21 years and the girl should be above 18 years as per the present rules.
It is also illegal to marry, as per the recent High Court decision, without the consent of Parents. Both can be sent to jail along with penalty (imprisonment or paying a fine).
Be ready to face the consequences. There is no via media now.
It depends on your luck and the help by the staff of the Marriage Officer.