My flooring guy says it is because the old house was not heated before he started working, and since I moved on the coldest (8 below) day of the year, the poly did not cure properly. He said to watch to see if it goes away.
See, that is the problem when people who are working in an industry never actually learn the science behind what they're doing. Experience alone is great, knowledge alone is great, but combine the two and you have more than the sum of both parts.
Do this: Clean the "oil" off the floor with a damp sponge and a minimal amount of water and see if the sponge and water start to turn "soapy" just as though you added a detergent to them. (Be sure to rinse out the sponge and pail first to ensure there was no residual soap in either to begin with.) If the water starts to turn soapy, read on...
If this was a water based poly, what you're seeing isn't "oil" at all.
Believe it or not, it's soap. But not real bath soap, like Ivory, Dove or Irish Spring.
It's a surfactant. Water based coatings (as I'm assuming you had a water based poly put down) will have surfactants added to them to lower the surface tension of the coating so that it "wets" the surface (the wood) better, and therefore bonds better to that wood.
In latex paints, this phenomenon is called "surfactant leaching" or "surfactant exudation". It can occur when the temperature turns cold or the humidity increases or the paint gets wet shortly after the paint is applied. The result of the paint getting wet or cold, or even being exposed to high humidity is that the surfactants in the paint film will migrate to the surface of the film and dissolve in any moisture or condensation on that surface. Then, as that water or condensation subsequently evaporates, the surfactants are left behind as an oily sticky substance on the surface of the paint.
Surfactant exudation normally shows up within a day or two after the paint dries, but it may show up after that as well since the surfactants remain mobile in the paint film. They just need something to draw them to the surface, like water on the floor from being wet or condensation forming on it.
I think what may have happened in your case is that the floor got very cold the day the movers moved your furniture in (cuz cold air sinks). After they left and you closed the door, the house may have warmed up, but if the floor was still cold, condensation may have formed on it. That may have caused the surfactants to migrate to the surface to dissolve in that water. Then, as the floor warmed and the condensation subsequently evaporated, the surfactants were left behind as a sticky film of what looked like oil on the floor.
If the floor finish is clear in colour and feels HARD to the touch, then you can be sure that the finish formed a film properly and the surfactant that's leaching out now is doing no harm to either the film or it's adhesion to the wood. If there was any harm done to the floor finish, you would have seen whitish clowdiness in the finish (in areas or over the whole floor) and the floor's surface being less glossy (or even flat) in those clowdy areas and it not being as hard as it should be so that you can scrape the surface of the finish off (even with your finger nail) especially easily in any white clowdy areas. Since you never mentioned anything about clowdiness in the finish, then I'm expecting that the floor finish is uniformly clear and colourless and hard. That tells me film formation was normal.
Probably the worst you can expect from this is that once you clean the soap off the floor with a sponge mop, some areas might be a little less glossy than others. You can correct this problem easily just by applying another thin coat of the same water based poly over the duller areas (or the whole floor if you want).
Here's a thread from a guy who was sure there was oil seeping out of his newly painted siding... until he tried cleaning it off with a garden hose and discovered it bubbled up and behaved more like a liquid dish washing detergent than an oil:
http://www.diychatroom.com/f4/x-90-siding-leaking-oil-now-help-25196/
Only, that guy was SURE it was OIL coming out of his newly painted siding. You're leaving open the possibility of it being something else by calling it an "oily substance". Congradulations, that was very open minded of you.
Clean the oily substance off the floor with a sponge and water and see if it makes the cleaning water soapy. That's really the proof of the pudding.