I have an Oregano plant and I have rarely used fresh oregano. Is it safe to use the oregano leaves shown in picture?
The dark underside is normal for some varieties, but the white on top is another matter. It could well be powdery mildew which while seemingly not toxic will spoil the eating qualities, or it could be mould from damp storage. I'd look for better leaves elsewhere on the plant. Here's a little more detail
Fresh oregano is a wonderful herb, there's no reason you can't use it, just wash the leaves with clean water beforehand to make sure they are free of soil or other contaminants.
In the case of the leaves shown in the picture some look like they have fungus growing on them, they are probably safe if cooked but I wouldn't expect them to taste very good. Use the non-fungus ones and discard the rest.
If your plant has lots of fungus it may be in a very damp area and not getting enough sun. Don't be afraid to aggressively prune it back to get rid of the bad stuff so it can concentrate on new growth.
Your post suggests that you just picked these leaves. Please check your plant to see if any other leaves are coated with this mysterious white substance. If so, your plant may be affected by an insect, insecticide dusting, or fungi. All things that you should address.
If you have a County Arboretum nearby, you could consult with them. Take a sprig of the infected plant (preferably in a zipper type bag) to the Arboretum and ask for their opinion and advice. Sometimes you only need to spray the affected plant with a diluted dish soap. But you should determine what you are dealing with first.
As far as using the leaves you've picked: use caution and clean them thoroughly.