I have an Oregano plant and I have rarely used fresh oregano. Is it safe to use the oregano leaves shown in picture?
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.
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