Nikon D7000 can be bought for a similar price to the OM-D, the sensor size is similar, plus the physical size is also similar. For image stabilisation it's not going to make a massive difference if you can hold it steady with two hands. I suspect if you want a steadycam device then the internal stabilisation is not going to achieve what you want.
I shoot video on my D800 and it comes out nicely, and it's not hard to get good handheld shots if you plan your shot. It really depends what you are shooting.
Also, since you have a lot of Nikon lenses, you can still use it on the D7000, and it you have some nice fast lenses then you will enjoy getting the shallow depth of field with some good primes like a 50mm.