There's a relief valve on the oil pump which opens when the pressure reaches a preset level. Historically this was achieved by nothing more than a coil spring. I suppose it could be fancier these days, but the principle is the same.
Overfilling can aerate the oil and reduce pressure if the big ends touch the surface, and can contaminate the cat, but I've never hear of an example of this.
Someone I know had a fuel system fault on a Mini. Overnight the fuel tank siphoned a large amount of petrol into the sump. Even with this, it started and ran roughly. I don't remember if there were consequences though!
