Hello and welcome to the OB
Well I use all types of paint, but I have not painted with oils in the same room with my Orchids yet.
I would guess with enough ventilation you should be all right, none of my other plants have suffered because any panting and such that I have done in the past. But then when using high "fume producing" products I always make sure I have good ventilation.
I'd also presume it would depend on:
What types of Orchids you have?
How big your painting is?
How much paint and turps you are using?
How big is the room you are painting in?
How often or for how long will you be working on the piece?
and
How much ventilation is available?
Put it this way, if the fumes are affecting you then they are more than likely affecting the plants in some way. But that is an assumption and without experimenting I can not say for certain (I may experiment with this sometime in the future).
Be careful though that the ventilation does not cause any "detrimental" cold drafts! Depending, of course, on the care the particular Orchids need.
Anyone else know for certain?
(Izzie's suggestion of protecting your precious plants is always good though
)