The National Interest covers the invasion scenario nicely here. It is unlikely, due to the atomic weapons N Korea has, and probably a substantial supply of chemical weapons as well. The heavily populated city of Seoul is very close to the border, and would likely become a target of revenge with very high civilian casualties.
China recently positioned a higher number of troops on the N Korean border, but the purpose appears to be more to stop a mass emigration, than to invade.
Invasion? Doubtless, both the US and China have contingency plans for invading N Korea, but the chances either would actually do it are unlikely.
A more practical and safer scenario would be to kill Kim Jong Un. He has executed or driven off anyone of any real leadership ability in his government, so with his demise, there is no one who could step in and rally the troops to whatever the cause of N Korea might be said to be.
A precision strike is a possibility - Kim is still seen in public on occasion. One idea floated was to offer his military leaders a big bundle of cash and permanent residence in any western nation they choose, if they'd kill him and walk away.
It will be very interesting to see how the major powers handle this situation. When Kim threatens to use nuclear arms, he must be taken seriously. The results of the N Korea issue will have a large bearing on whether other semi-rogue states pursue nuclear arms. If the major powers can take out Kim without an invasion, they can demonstrate that nuclear arms do not protect the person who threatens to use them.