Here are the oil and gas companies that only sponsoring F1 teams but not a de facto fuel and lubricant supplier:
CEPSA with Scuderia Toro Rosso in 2011-2015.
PDVSA with Williams F1 in 2011-2013.
Petrobras with McLaren in 2018 only.
PDVSA with Lotus in 2014-2015.
Pertamina with Manor Racing in 2016.
Repsol YPF with Arrows in 1999-2000.
Any additions?
Here's the reasons why oil companies not electing supplying fuels and lubricants for F1 teams as i mentioned above because of funding either driver's personal sponsor. Example: Toro Rosso partnered with CEPSA in 2011-2015 despite the team using Shell fuels in 2011-2013 later Total fuels in 2014-2015 because of Toro Rosso's financial rebuilding progress after buying Minardi in late-2005.
Repsol sponsored Arrows F1 in 1999-2000 despite using Elf fuels because of Pedro de La Rosa's personal sponsors AFAIK.