Assumption 1: Force is applied contrary to its revolutionary movement.
Well, the minimum work done needed to move the earth would be the equivalent of its kinetic energy.
I say minimum because the total energy will be zero, before the sun's force of gravity pulls the Earth towards it.
More energy will be required to actually move the planet away from the sun though what that may be is currently beyond my abilities.
The mass of the Earth is 5.972 × 10^24 kg.
The orbital velocity of the Earth is, according to the Institute of Physics, 30 km/s.
KE= 1/2mv²=0.5* 5.972 × 10^24*30 000
Therefore, the Earth's kinetic energy= 2.65*10^33 J
This is planet level. The lower end of this particular tier to be exact.
A character may not need to overcome the kinetic energy at all, however, but instead move the planet out of orbit by pushing in the same direction which would be a more economical method of achieving the desired effect.
I remember reading a scan where The Flash had to literally tackle Kid Flash out of mid-air (presumably to apply a counter force) because the former had managed to reach escape velocity and was understandably panicking at the prospect of being projected into outer space to do anything about. You can probably tell where this is going.
Assumption 2: Force is applied complimentary to the direction of revolutionary motion
Escape velocity is that which is required to overcome the gravitational pull of a larger body.
Well, now I have to calculate the escape velocity of the Earth from the Sun using the universal gravitational constant, G, the Sun's mass and the total distance between the two heavenly bodies.
ve= Sqrt 2GM/r=2*6.67*10^-11* 1.989 × 10^30/1.5*10^11
Ve= 42 058 m/s
Finally we can use this to find the energy inputted into the system: 1/2 mass of earth * (42 058 m/s - 30 000)^2= 4.342*10^32 J
This would result in the Earth being projected at a tangent into space at dizzying velocities. This is hardly portrayed in fiction.
Energy needed to move a planet out of orbit without stopping it beforehand: 103.7 Zettatons
Energy needed to move the Earth as usually portrayed in fiction: 633 Zettatons