So, if it is one of the oaks (...)
It's not an oak, since it's lacking the ray flecks. Google "oak ray" to see what I mean. It's a really tell-tale sign in oak.
looks like Black Cherry to me. Ring porus, darkish heartwood, flakey, platey bark.
Cherry is diffuse porous...not ring porous like an oak species. From the first picture, I really can't see the pores, so I don't know if it's ring- or diffuse porous. Lars, can you tell from the end grain?
I'm pretty sure that second pic is a black locust piece. Is the first pic from the same tree? I don't think so?
If you happen to have a UV black light nearby, put a piece of heartwood under it. Does it appear fluorescent?
Lars, I have to ask...do you know what you Dutch last name "Groteballen" means in English?