I want to spray a stairs with pc cellulose paint .It was previously varnished with oil based varnish

Oil based paints and varnishes should be thinned ideally with turpentine, turpentine substitute (white spirit) or with a propriety thinner for synthetic coach finishes.

Depending on the spray system you are using will depend how much thinning is needed - usually no more than 10% unless a low pressure compressed air or airless sprayer is used. Accuracy produces the best results and accuracy can only be achieved using manufacturer's recommendations and a viscosity cup and a clock or watch with a second hand.

One word of warning; when spraying oil based or synthetic finishes the overspray or spray mist remains "wet" for a considerable time and will adhere to whatever it touches or settles on including skin and nose hair. A Tyvek overall with a close fitting hood is not expensive and these days a decent filter mask is fairly inexpensive.

I have little experience of oil based stain other than knowing it is supposed to give long-lasting protection without further covering.

I prefer to use a spirit based stain and find it gives good results and once the spirit has evaporated it is quite inert and won't interfere with any subsequent finishes overcoating it, in fact it is designed to be overcoated.

I have used a water-based varnish and I found it particularly unimpressive compared to the usual alkyd resin or oil based stuff and it will be a long time before I use it again. Buying coloured varnish would mean you don't need the stain. I haven't tried it but I think a small amount of spirit stain could be added to oil based varnish...

The best bet is to leave the oil poly on the treads clean it up and refinish it .
However if you need to paint for what ever reason I would recomand grinding back to wood its a lot of work pine or oak treads .
But the problem is stairs get a lot of LBS. per sq/in .In a small area of the tread and depeneding on how high of a traffic area it is nothing will stick to oil poly or varnish.
Strip them and go with an epoxy system .
And by the way I have running comerical paint jobs for 40 years

1. The switching pawl (lever on the top cover that switches from zigzag to cam patterns) may be engaged in the cam or automatic pattern side. Check that first.
For zigzag application, the lever must be engaged in the zigzag side (lever pulled back toward the operator). The stitch width dial is then used to provide your choice of width.
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2. It is common, due to oil varnishes, that the switching pawl that is actuated by this lever is stuck between the zigzag and the automatic position, thus preventing the transmission of power to either the zigzag cam or the automatic pattern cams and to the needle.
The best way to detect this is to remove the top cover. You can then switch the lever back and forth to observe if the switching pawl engages firmly into either of the receiving forks. If the switching pawl is sticking, a few drops of certain solvents are applied by a technician on the switching pawl support. The switch lever can be rapidly switched back and forth until you see the switching pawl engage into the receiving forks and you hear a crisp clicking during each engagement. This repair can be permanent or it may create only a temporary fix due to the amount of oil varnishes on the parts.
If the machine is heavily varnished, it suggested that the parts be disassembled and cleaned for flawless performance. If the machine had been sprayed with WD-40, petroleum based solvents like mineral spirits will not break down these varnishes.
A caution regarding solvents...DO NOT USE (WD-40) as your solvent. WD-40 is a marvelous product for its intended application as a water displacement device. It is not to be used for lubricating a sewing machine. Note: "Bernina Technical Information bulletin #1" issued in 1982, forbade the use of such spray lubricants and solvents. SewTechnical Home

Check to see if the varnish you used is a sun curing varnish, if it is, yo may need to get some sun lamps to get the varnish to cure. If that isn't the case, you may have to remove the varnish and use something more suitable for the countertops.

Look at the back of it to see if it has yellowed. If there are yellow stains on the frame and the back, then it is not the varnish in the oil paint that has yellowed. You can then use something like 409 cleaner to get the stains off. You should blot the painting and not scrub or wipe it. If the varnish is yellowing you can get a product called conservationists liquid and apply that as per the directions to help with the varnish problem.

Yes, you would need to remove the varnish before you painted it otherwise the paint would not take
to the wood and run, it would look very messy. My advice is to take the armory apart and sand, clean
and paint each piece separately.

did you recently paint with oil based paint or varnish? that's where the smell will come from.