Is it obligatory to pray the missed salaats in order ? What if one has much missed salaats ? When is the obligation in the order waived ? Is there any differance in the ruling of ''old missed salaats'' and ''new missed salaats'' ?

In the name of Allāh, Most Gracious, Most Merciful  

Assalāmu ῾alaykum wa Rahmatullāhi Wabarakātuh  

If a person misses lesser than six Salāhs besides the Witr Salāh i.e. one complete days Salāh or less, it will be necessary upon him to perform his missed Salāhs in order before performing the current Salāh.

(Hāshiyatut Tahtāwi ala Marāqil Falāh, Pg.440, Ilmiyyah)^[1]

Once he misses six Salāh besides the Witr Salāh i.e. more than one days Salāh, it will no more be necessary upon him to perform his missed Salāh in order. 

(Nōrul Idhāh, Pg.105, Qadīmi)^[2]
  (Raddul Muhtār, Vol.2, Pg.68, HM Saeed)^[3]
(Hāshiyatut Tahtāwi ala Marāqil Falāh, Pg.440, Ilmiyyah)
(Fatāwa Tātārkhāniyyah, Vol.1, Pg.758, Idāratul Qurān)

If a person already missed six Salāh or more, there is no differentiation between the old and the new missed Salāh. It will still be obligatory upon him to perform Qadhā of those Salāh, however, it is not necessary to maintain the order until he completes all his missed Salāh.

(Fatāwa Tātārkhāniyyah, Vol.1, Pg.758, Idāratul Qurān)

And Allāh Ta῾āla Knows Best

Checked and Approved by:
Mufti Ebrahim Desai
Dārul Iftā