Engine Burning Oil problems of the 2007 Honda Accord

My car has had engine issues for the last almost 8 years. Burning oil at a massive rate. It also stalls with this sudden jerk and rocking sensation when accelerating/shifting at a low speed. I bought my car brand new but first began experiencing this rocking sensation in November of 2008 while driving down a slight incline at a low speed on a street. This rocking stopped on its own for quite a while. Then in April 2011 it began again where at Honda's diagnosis and recommendation they took my engine apart and �fixed� the problem when it later arose in 2014. This issue has now escalated to the engine stalling when I drive over 80 miles an hour - acceleration suspends until the speed drops back down to 70 miles an hour. It's so unsafe but became predictable and normal. In all of this my check engine light will not go off hence causing the car to fail emissions tests. I have brought this up to my local Honda dealership along with excessive burning of oil. I have performed the oil consumption test for the dealership to say that my consumption - though clearly excessive and very dark - is technically within Honda's parameters. Every time I re-visited either issue I was given the run around and now deemed by many mechanics even at Honda to not put anymore money into the car. The diagnoses went from O2 sensor to cam chain to now the rocker arm. In 2014 when Honda supossesly �fixed� the cam chain I was explicitly told that this was the reason my car jerked and rocked but clearly that was a fabrication. My car presently burns at minimum 2 quarts of oil a week. Upon recent research I saw a recall on 2007 Honda accor engines for stalling but my VIN number was not included.