I wouldn't use essential oils. That will likely just gunk up your machine and might be reacted to anyway.
White vinegar in the fabric softener compartment, and making sure the machine is vv clean as Delilah says (I tend to do a 60 degree wash fairly regularly with things like face cloths, bedding, cleaning cloths, and any clothes which are holding onto a damp or BO smell, and then I do a 95 degree wash with the machine empty with some anti-limescale stuff in it about 2-3 times a year) and then getting clothes out ASAP when they are done is important.
The vinegar I actually find is the best thing ever for helping clothes smell fresh, it kills germs, kills some mildew I think too and helps reduce limescale in your machine. You could try different brands of powder too, though it sounds like you already have tried this.
What helps me get clothes out ASAP from the washing machine is using the "delay start" feature so I know I'll be around, and not busy, when it finishes.
The other thing you can do is if your washing machine has a rinse hold function, use this if you're not sure if you'll be free when it finishes. Rinse hold keeps the clothes in a tub of water until you're ready to come and press the button again and then it will do the final rinse and spin which takes about 10 minutes. This prevents it from getting mildewy.
A bit of a nuclear option, but I also found that getting a tumble dryer was my best thing ever - when I had to hang washing up, I'd often procrastinate emptying because I knew I'd have to stand for 20-30 mins potentially taking the old washing off and then hanging the new washing up. Whereas putting clothes into the tumble dryer means (at worst) open the door, pull all the contents into a clean washing basket, then fill with the wet washing, empty fluff/water trays and turn on. So I don't procrastinate on this and my washing doesn't sit around damp for hours.
If you don't have a TD the two strategies for trying to get it out and hung up ASAP help - and I used to sort of plan my washing around a "wash day routine" where I'd put one load in first thing in the morning, then cue up a ~1h podcast and when that load finished, do this in order while listening:
Collect new load
Remove old load
Fill new load, start wash on shortest full wash (~60-90 mins)
Carry wet washing to airer
Take down old, dry washing into piles
Hang up new, wet washing
Put dry clothes away
Fetch second load from washing machine, hang up
Lastly make sure the airer is a good design - not one of the "stacked up Xs" because the washing will drape over each other and not get proper airflow. Tower airer, balcony airer (either sold in Argos and Ikea) are good designs. Tower takes up less floor space. Locate in the warmest room and/or with best air flow. Dehumidifier or extra heating in that room while drying can help.