Noticed several times that my clothes smell like oil. Why?

Sounds like the clutch may be slipping. Does it go into a high speed spin?

Try drying your clothes without the dryer sheet and see if the smell is still there. If it is not, then the problem is the dryer sheet.
If it is, then you need to describe the smell better. Different people handle smells differently. What smells musty to you may smell fragrant to others.
You need to determine if the smell you don't like is really a musty smell, or is it a fragrance you don't like. Have some friends (not family members) smell the clothes and verify if what you are smelling is musty or fragrant.

It could also be that even though the clothes smell OK out of the washer, that the detergent you are using is the cause.

Hi.
I am not a professional fisherman, but I like fishing. For that reason when my clothes smell fish, that means that I caught a good prey, I am happy about the smell and throw the smelly clothes to my wife. I never thought about the problem.

However, after reading your question I had a look on the Internet, and I noticed you already tried the most popular solutions.
I found this thread , where poster are suggesting a number of remedies to get rid of the smell. Have a look. You will need to scroll down the page to find suggestions.
All the best.
G.

Run a wash cycle (no clothes), with a cup of baking soda, regular detergent and hot water. Leave the door open after each wash day to dry the interior which helps prevent mildew returning.

If you open the door of your Neptune, you'll notice a small trough between the door gaskets (inner and outer) There is a drain at the bottom that can get blocked by lint and other funky stuff. Next time you do a load of towels, take a small dirty towel and wipe that area of your machine out real well. Secondly load a slightly smaller load in your machine. Be sure to use a HE compatible soap...less foaming- it does make a difference.. Also the swishy slushy sound is normal and there is liquid in the drum for balancing...it's normal.. I think with a clear door drain, a bit smaller load .you'll find it won't be smelly.. I've got one of these and the only time it gets ordoriforous is when I've jammed it to max capacity. Let me know if all this helps you out. k

hi.
not sure if this link will help you find out why,but have a look.
After wash clothes all smell like oil gas from machine Google Search

mostly that after burn,,check vent and vent exhaust reall good,,exhaust coming back in home..

There is a seal between the compressor and the motor that in failed condition will leak oil into motor windings causing burnt oil smell. Some hitachi compressors suffered from failed valves or head gasket causing extra heat but not oil smell. These compressors also have a thermobreaker built into the windings that when failed will prevent motor from starting or would start and run for only a few moments then open. This part is not replaceable. enjoy

most of the time this smell can be taken care of by adding white vinager to the wash cycle through the soap dispenser whil e it is running. you may have to use quite a bit to do the trick, and even run it through several times. the second thing you can do is if you arent already, leave the door ajar when the machine is not in use so it can breath so to speak. hope this helps