Janet, you have Asiatic Lilies on your first picture. The orange one is probably 'Loreto'. The white Oriental on your second picture is most likely 'Casablanca'.
The red Asiatic is not distinctive enough to ID, sorry.

Alina thanks for the info. I looked up 'Loreto' and it sure does look like those I have.
Those are done blooming now, so I'll have to wait until next year to get a better picture of the red ones.

So I wonder if the Oriental lily was in with the other lily bulbs I planted and just dormant for the first couple of years? It was quite a surprise when I noticed it coming up with them as I could tell it was a "different" kind of lily.

It's very pretty though and the fragrance is strong. Would it hurt it any to dig it up after it's done blooming and replant it somewhere else? Would fall be the time to do it?

Thanks again,
Janet

Janet, it is not about the picture. There are too many solid red Asiatics to define which one you have.
The Oriental could be dormant or just too small to bloom. You might not notice a bloomless stem among other Lilies. Fall would be a perfect time to transplant it.