I’m new to the forum and now realize these issues are fairly common. My 2010 with 232,000 just started to get the engine vibration when accelerating and is burning oil. I’m not sure if it’s worth getting fixed or if I should sell it. I’m not comfortable doing the work myself.
It sounds like the EGR System needs to be cleaned. At 232K, it's probably clogged. If you can DIY, clean it, there are many videos on this topic. See @NutzAboutBolts videos in the maintenance section. If this work is not performed soon, the head gasket will probably fail soon due to excessive engine heat. If DIY is not your thing, then your best bet is to move on, replace the car soon.
1.5 quarts in 6,000 miles is not bad for an engine with so many miles. You should be changing the oil at 5K miles. So this really is not bad.
The oil consumption isn't that bad for a car with that mileage, I would at least have someone see what the problem is. It is the cheapest option, don't throw the baby out with the bath water.
When you have under 5 posts, they do not show up automatically . Having a location listed on your profile can help get local support when required. Have you tried any local shops or know any mechanics in the area? I’m not sure what mechanics there are around, but @danlatu and @wjtracy arent too far away and might have more to offer.
Burning engine oil tends to fowl spark plugs. Incomplete combustion will cause engine vibrations and may not throw a code. Did you install new plugs @200k. Is you egr cooler, pipes, egr clean and the ports that go through the intake plenum? A compression test would also show an imbalance of combustion on all cylinders. If your compression is low on one cylinder because a valve does not fully seat will cause crazy vibrations. I would start with a full cleaning first.
Plugs were done at 200,000. EGR cleaning has not been done. I have experienced a cold startup engine shaking in the past, no codes right now. What it is doing now is different, more of a rattling/knocking during acceleration. I’m just trying to decide if its worth putting money in to and see what other people have done when they get this many miles.