Yes you can surely get EEE branch in  National institute of technologies, but that NIT might not be of your choice. For EEE branch you will have to wait patiently till the 5th round counseling, and you may be into one of the NIT. For this you will have to fill out the josaa counseling form carefully. If there are any NITs in your own state then you will not have to worry alot as you will be eligible for the home state quota as well which will further ensure your selection.

For ECE branch, your rank is a bit low for NITs. You can surely try till the spot round if you are extremely dedicated to this branch and NITs but in my opinion you should also go for the other government colleges which give admission on the basis of the JEE main marks. You can get a branch of your choice in these colleges.

Good luck!