Pokeberry = Pokeweed?
Pokeweed (and all North American Phytolacca spp.) have alternate leaf arrangement.
The seedling true leaves are opposite.
That the seedlings seem to be everywhere is typical of ash, and even if it is not, they must be a common plant. Green ash seedlings (the only species I am familiar with) normally begin making compound leaves by their third or fourth set of true leaves. By that time, also, a woody stem should be unmistakable.
