Can someone please tell me that, is istinja' (الإستنجاء) for ablution is necessary or not?
Istinja is the Arabic term for cleaning away whatever has been passed from the urethra or anus with water, toilet paper or both. (Wikipedia)
Praying with najasa on clothes or on najasa
First of all, you should know that according the mawsu'a al-fiqhiyya a prayer is invalid if you prayed on a najiss thing or soil or wearing something najiss knowing this. If you didn't know or forgot it and prayed then the prayer is considered as valid. If somebody realize he/she is praying with najassa and could take it away or take away the tissue which is najiss then he/she should do so, if he/she couldn't his/her prayer is also considered as valid.
Definition of Istijmar and istinja'
From this point of view, you should before performing wudu and at best when you visit the toilet do istinja' or istijmar. They are defined in the mawsu'a al-fiqhiyya as follows (My own translation take it with care):
الاستنجاء: هو إزالة الخارج من السبيلين بالماء الطهور.
Istinja' is to remove what comes out of the two orifices of the body by using clean water.
الاستجمار: هو إزالة الخارج من السبيلين بحجر، أو ورق أو نحوهما.
Istijmar is removing the same, but using a stone, paper or something similar.
Note that istinja' is the most preferred way to remove such najassa, so if water is present you should at least use it even if you performed istijmar, istijmar is usually allowed or one may say "preferable" if the najassa can be easily removed, which means you won't have to clean up that much!
When is istinja' (this also would apply for istijmar) necessary?
If you had urinated or defecated!
In any other case you can start your wudu without istinja' unless you have already performed it after the described act or still feel some najassa on your body! Read also the opinion of Imam Malik on what to do after urinating from his Muwatta'.
Finally here some ahadith about the matter:
From Sahih al-Bukhari: prohibition of using the right hand for istinja'.
From Sahih Muslim : the Messenger of Allah (peace be upon him) used water for istinja'.
From Jami' at Tirmidhi: etiquette of defecating.
From Sunan ibn Majah: Using three stones for istijmar (da'if).
From Sunan abi Dawod: Using the left hand for istinja' and prohibition of using the right hand.
And some other references:
A fatwa in Arabic on how the Messenger of Allah used to do istinja'.
A fatwa on bathroom etiquette.
A fatwa answering if it is permissible to perform istinja' with zamzam water.
And Allah knows best.