NIT

Yeah, you can. If you score good in JEE Mains and advanced, then you definitely got NIT or other government colleges and for the rank, you can check here: https://www.resonance.ac.in/answer-key-solutions/JEE-Main/2017/jee-main-2017-rank-predictor.php

You have great chances to get NITs if this is your All India Rank. The cut off scores based on caste decides your chances to get the top NITs. If you have scored way more than your cut off then you can get good NITs.
The caste wise cut off is:
General (OC)-81
SC-32
ST-27
PWD-1
OBC-NCL-49
You can apply for counselling through www.josaa.nic.in
You are qualified to appear for JEE Advanced.

The counselling will start only after the JEE Advanced examination.
The date for JEE Advanced will be at the end of May. So you have to wait till that.
May be the counselling for JEE will be from second week of June only.
Apply for counselling through www.josaa.nic.in

Hopefully, this will help you:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You can predict your rank and college with the help of the links given below:
1. Rank predictor: https://www.shiksha.com/b-tech/resources/jee-main-rank-predictor
2. College predictor: https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

You have got good marks, but NIT, Surthkal, Karnataka comes under the top list of NITs.
Not only this, they both are famous for their mechanical branch after NIT, Durgapur and Surat.
So, 139 is not enough as the admission in those NITs starts from 180+ for home quota and 250+ for other state students.
But as you mentioned you are an OBC category student, you have very slim chances to get into it.
I will prefer to give them top priorities in the choice filling.
All the best.

For getting into IIT, you must qualify JEE-Advance.

Try the below link of Shiksha:
https://www.shiksha.com/b-tech/resources/jee-mains-college-predictor

Yes, you can get it but you have to study B.Tech first year again.

Hi Yash Anand,
You belong to the OBC category, so you have scored more according to your cut-off marks of 49. You can easily get NITs, but not the good ones.
You can apply for counselling through www.josaa.nic.in
If you don't get any of the NITs, you can get IIITs or GFITs.
These are also government colleges which admit students through JEE Mains.
All the best.