Will a box that it's is mass is grams float in olive oil?

Answer 1

To float in olive oil the box needs to displace a volume of olive oil that has the same mass as the box - the less dense the oil (for example by being warmer) the more volume the box will need to displace to equal its mass. If it cannot displace a volume of olive oil that equals its mass, the box will sink.

Or to put it another way, the box will float in olive oil as long as its density is less than that of the oil.