What is high energy physics? 
*

*Is high energy physics the same as particle physics? 

*Does research in high-energy physics include things like quantum gravity, string theory and quantum field theory? 

*Is unifying the four fundamental forces one of the aims of high energy physics?
 A: Elementary particle physics is an outgrowth of what was high energy physics,  historically  at the time.
X-rays were high energy physics when first discovered, they are part of the tools of solid state physics now.
Alpha particles and gamma rays were high energy physics at their time, they are nuclear physics now.
Mesons discovered  in cosmic rays started the study of particle physics showing elementary particles were more than electrons  and photons and that protons and neutrons were not elementary.
At the present time LHC has the highest energies in the laboratory, and the newest elementary particle discovered is the Higgs.
The high energy label is connected with the Heisenberg uncertainty principle 
$$\Delta x \Delta p \geq \frac{\hbar}{2}$$
$$\Delta E \Delta t \geq \frac{\hbar}{2}$$
The higher the scattering energy in the experiment the smaller distances that can be probed.
That is how we found that protons were composites of quarks, by scattering with higher momenta and studying the crossections. This program is going on to higher energies.

Does research in high-energy physics include things like quantum gravity, string theory and quantum field theory?

String theory yes, if we are lucky we will find traces in the current LHC runs. Quantum field theory is the underlying theory of particle physics, not a point of research, rather a mathematical tool. Quantum gravity needs cosmological energies and distances, though string theories extrapolate to those energies.

Is unifying the four fundamental forces one of the aims of high energy physics?

Yes.
A: As an alternative to Anna's nice historical discourse a heuristic that covers modern uses of the phrase would be that energies are "high" when the QCD can be treated as perturbative. That regime sets in considerably above the nucleon mass scale, say 10s of GeV.
So LHC physics is in, JLAB physics is out (even with the 12 GeV upgrade).
