Define, "soggy soil". Do you mean occasional standing water? Important, because standing water would eliminate many possibilities. Also, there is a cold-hardy, native Pa. Myrtle (not sure how it compares to the southern species). I like Aucuba japonica for shade, it would work in zone 6b plus, but not in "soggy" soils. The one in the picture is right outside the shower, so gets plenty of water, but would not describe the soil as soggy.

You could try Osmanthus americanus (Devilwood). It's native to zones 8-10, but some sources say its hardy down to zone 5.

Poaky,
You have a native form of southern wax myrtle up where you are.
It's the same bush, only the zone 6 version.
It's Bayberry. Yes, just go find a Bayberry bush up
where you live, it's the same thing as wax myrtle.
Wax myrtle has the berries too. They smell like bayberry.
You know, I would plant one and try it.
I do know they love sun though, but just try it and see how it does.
Southern wax myrtle won't make it where you live, even with climate change.
I would buy a bayberry, same thing.

Thanks for the replies, I will try Bayberry, Wiki says wet soils are okay for it. The Devilwood was listed as zone 8 +, and said to grow in zone 7, and Daves garden said Kentucky in Georgetown, Lexington and Louisville, which the last 2 are zone 6 according to a map for Kentucky gardening zones, so I may try both. It is for an area that stays very damp unless we have less rain than the past 3 years. Some areas are standing water a couple inches during the growing season, or after winter precip melts or is rain. If we have less rain it may change. The area is the lower yard area. I have an area upslope for well drained lovers like Rhodies. I want my yard to be shaded with beds including some shrubs at the top and the sometimes soggy bottom, so I will need some shrubs for the soggy bottom, the years it is soggy. It may turn around and not rain much for several years here, and rain where there has been drought, but it has been soggy the last 6-7 years, at least. One area has an underground spring, so will remain moist, I think anyway. My goal is to be able to to have most of my yard shaded, except where I have veggies growing. I may be dead or old before some trees get that huge. I love the Bayberry thought. I can make potpourri with it and some evergreen Mag leaves etc.

Ilex glabra (Inkberry or Gallberry depending on location) grows on wet sites down here just fine. I think its native all the way up the east coast.

Inkberry is a terrific native with a vast range, and readily available at the big box stores. Love it!

Thanks, Alabama and Njoasis. I'll have to check out inkberry. There is enough area to cover that using all the mentioned plants may be possible. {{gwi:328485}} Is this an inkberry? Or do they look like this? I took this pic in 2012. It was growing away from any houses, near a white oak. Do they all have blue berries?

This pic of waxmyrtle is in Wash DC. They maintain them at 6-7' by cutting them back every winter which means they have zero winter interest and kinda defeats the purpose.
I've seen acres of wax myrtle on Assateaue/Chincoteague Islands, Cape Henlopen DE AWA coastal NJ. They are always in full sun.
Rosebay Rhodo would be a better choice, its native for us growing in low lying areas along stream banks. You're only problem here is finding Rosebay in the trade.
Regarding Ilex glabra I agee with the others, a great shrub, black fruit, some compact forms available. We see Inkberry now planted around libraries, office buildings and commercial parking lots.
{{gwi:328486}}

I have 2 Rhod. max already. I would use them but I would need to make a mound to grow them on. I put that in my original post. I know sometimes when you read a lot of posts and skimming through all of them, it's easy to miss important things already mentioned, I'm sure I've done it many times. I think if they were planted up on a bank, the stream or whatever pooling water underneath is ok, but directly on the ground with soggy soil or pooling water for several days before drying out on a regular basis may rot their roots. The Rhod maximum would be my choice if not for the soggies and full sun for now. I found the 2 Rhod. Max I have: one was locally wild dug and the other I got from Rarefind nursery. I tried from seed and failed. I am glad for the suggestions, especially the bayberry. My evergreen mags have nice smelling leaves, so adding some bayberry to them and other stuff that I don't know about yet, will be fun. For potpourri or making soap, if I can soak the leaves in olive oil and the scent transfers to it. I used to make my own soap, but have been lazy for a couple years.