Yes , surely you can apply for all the PSUs with the current backlogs for any branch of engineering , just the condition is that you will have to clear all the backlogs before the counselling procedure starts or any kind procedure from the PSU starts .

I would like to suggest that it would be best if you clear all your backlogs in 7th semester .

Now generally , PSU like HPCL,  need min of 60% in B.E or B-tech for open category or OBC ( non-creamy layer ) and 50 % for SC/ST/PWD.

Now ONGC has a criteria of minimum of 60% in bachelors in all the categories.

But PSU like IOCL has criteria on minimum of 65% in bachelors for open and 60% for SC/ST/PWD .

So, my suggestion is to have a 65 % in Bachelors for open category and OBC ( NCL) and 60 % in SC/ST/PWD .

Talkin about the gate cut-off , you can visit the link given below for detailed analysis :

https://engineering.careers360.com/articles/what-are-gate-scores-for-psu-recruitment

hope it helps .