Let's start with the weight of the house, most house movers I know say the max weight of a moveable house is 70,000kg. Let's say ours is a little smaller, 40,000kg.

A standard 1 liter balloon can lift 1 gram. This is found by using the ideal gas law, first explained by Émile Clapeyron in 1834, PV = nRT. or:

pressure multiplied by volume equals the amount of gas multiplied times the temperature. In other words, the temperature multiplied by the amount equals the pressure in an equal volume

You see, gas is just particles flying around, so if the same amount of particles get flying around in a smaller space or volume, they bounce around more, causing more force, and they get hotter(like they're in the gym turning up the treadmill). Helium has smaller particles bouncing around than air.

Therefore, helium is less dense than air, and it is contained in the body of the balloon. As explained in archimedes principle, a less dense body will float, or experience a buoyant force in a more dense one. And, 1 liter of helium at the density of helium, .16 grams per liter, is less than the density of air, 1.18 grams per liter. So, at the same temperature, the force of gravity(mass times acceleration of gravity) is 1.18-.16 = roughly 1.02grams lifted against gravity, or floating.

So, for 40,000kg, lifted by 2 liter helium balloons each lifting 2.4 grams, you'd need at least 17,000,000 balloons.

Now, you'd have to take into account that some balloons would be popped, and wind may create downward force you would need to overcome.

first let's look at the wind pressure. The Ensweiler equation shows the pressure of wind. Let's say the bunch of balloons is hit by 50mph wind. 50mph^2 times the constant .00256 = 6.4 pounds for square foot. converted to 31 kg/square meter. let's say that our balloon mass is100 balloons long, 100 balloons wide, 1700 balloons tall, that's roughly 17million. If a 2 liter balloon is 1 ft in diameter, or .3meters, then our balloon mass is roughly 1000 meters squared area. then that would be 31,000 kg of force, almost doubling the weight of the house!

I think it's safe to say that we'd need double the balloons, using the old engineering 2X safety factor. That's 32million balloons. Imagine that a flock of birds could take out 30%, and let's go ahead and jack that up to 50 million regular balloons.