Turbojet and turbofan engines are part of a family of engines referred to as reaction engines to emphasize the fact the aircraft is pushed forward mostly by Newton's 3rd law of motion when gases are accelerated.
Diagram of a turbofan jet engine, source
On which point(s) does the reaction force act?
The thrust produced by the engine is due to the net resultant of various forces acting on various surfaces of the engine. The thrust produced is a function of mass flow rate and the change in velocity ($T = \dot{m} (V_{e}-V_{\inf})$). So, both of these have to be taken into account, rather than acceleration alone. The location of maximum thrust generated varies with the type of engine.
For high bypass jet engines like those used by the modern commercial airliners, most of the thrust is produced by the bypass fan. Though the acceleration is not the greatest here, mass x acceleration is- so this is where the thrust is maximum. The maximum reaction forces are applied there
In case of pure turbojets, the (almost all of the) thrust is produced by the core. For low bypass turbofans, its somewhere in the middle, with the lion's share of thrust produced by the core.
Note that most of the reactive force is applied on the diffuser and the compressor due to the high pressure and the forward facing area (due to cross sectional variation) in this region. This high pressure also acts on the combustion chamber, increasing the reaction force.
In the turbine and nozzle, the variation in the cross section creates a surface area facing the rearward direction, where the gas pressure acts, resulting in an force applied in direction opposite to the compressor. The net result of all these forces gives the thrust.
Image from Aircraft Performance and Design by John Anderson; taken from quora.com
Most of the thrust is generated in the combustion chamber, followed by the compressor stages. The exhaust is only contributing a small fraction of the total forward gas load.
Source: the jet engine, Rolls Royce (ISBN: 9781119065999)
The picture show the gas load contribution of various parts of a pure jet engine. In turbofan engines, a relatively larger part is contributed by the fan.
The reaction forces are applied, strangely enough, to the fan disk as it produces the lion's share of the thrust by accelerating the largest quantity of air flowing through it; it is the actual object making contact with the airflow and pushing it out the nacelle outlet.
The low and high pressure compressor sections have additional reactive forces imparted upon them as the accelerate an air mass through them.
Reactive force is lost as air flowing through the gas core imputs a reactive force opposing forward thrust on the turbine rotors and hot section stators - the energy is extracted in the form of mechanical work to drive the fan/LPC/HPC.
On turbojets, low bypass turbofans, and to a small extent the gas core of a high bypass turbofan engine, the majority of the reaction forces are being applied to the fwd section of the jetpipe near at the last LPT stage or stator prior to entering the jetpipe due to the imbalance of pressure between this section of the engine and the exhaust nozzle outlet at atmospheric pressure.
For the very special case of engines operating in the supersonic region, a large part of the thrust is applied via the intake.
"The Concorde Air Intake Control System" via http://www.pprune.org/tech-log/426900-concorde-engine-intake-thrust.html :
A huge 75% OF THE TOTAL THRUST is produced by the intake subsonic diffuser section, this being due to the huge rise in static pressure that is occurring in this section. The 'negative thrust' from the forward ramp section this time is 12%, produced by the supersonic compression forces acting on the divergent section of the intake, resulting in an intake thrust component of 63%. So it can be seen that the vast majority of the Mach 2 thrust forces are transmitted to the airframe not via the engine mountings, but via the mountings of the intake, and to a lesser extent the TRA nozzle.
For every action in nature there is an equal and opposite reaction.
That sentence alone is incomplete and misleading, because this short version fails to mention the two-body system it was meant for.
The action and reaction can actually be swapped in position. The difference between a gas generator and a jet engine is the mere (over simplification) addition of the nozzle to accelerate the air out the exhaust.
So, you can confidently reverse the common sentence and write it as: the thrust on the engine (action) causes the mass air flow (reaction). And you won't be wrong.
The answer to your question; all the parts experience a normal force (thrust). Some are forward, some are rearward.
Shameless copy from Wikipedia:
Origin of engine thrust
The familiar explanation for jet thrust only looks at what goes in to the engine, air and fuel, and what comes out, exhaust gas and an unbalanced force. This force, called thrust, is the sum of the momentum difference between entry and exit and any unbalanced pressure force between entry and exit; looking inside shows that the thrust results from all the unbalanced momentum and pressure forces created within the engine itself. These forces, some forwards and some rearwards, are across all the internal parts, both stationary and rotating, such as ducts, compressors, etc., which are in the primary gas flow which flows through the engine from front to rear.
Transferring thrust to the aircraft
The engine thrust acts along the engine centerline. The aircraft "holds" the engine on the outer casing of the engine at some distance from the engine centerline (at the engine mounts). This arrangement causes the engine casing to bend (known as backbone bending) and the round rotor casings to distort (ovalization). Distortion of the engine structure has to be controlled with suitable mount locations to maintain acceptable rotor and seal clearances and prevent rubbing. A well-publicized example of excessive structural deformation occurred with the original Pratt & Whitney JT9D engine installation in the Boeing 747 aircraft. The engine mounting arrangement had to be revised with the addition of an extra thrust frame to reduce the casing deflections to an acceptable amount.
We see in this 3,000 lbf jet engine (image from Flight), each combustor has a net forward force of 50 lbf (difference between flame tube and outer casing). Having 16 combustors yields 800 lbf forward thrust along the centerline.
Other parts are treated the same way. Although I have to admit some are more straight forward than the other.
Let's take concept of energy for help. All jet engine thrust originate in combustion chamber (energy of burning fuel). Smaller or bigger part of this thrust ( depending on engine construction) is transferred from turbines blades ( high and low pressure) forward via axis to compressor / fan. Let's take example of low pressure turbine/ fan system. Expanding gas in combustion chamber pushes on turbine blade and via axis rotates fan blades. So any forward force created by fan blades is transferred via axis and turbines blades back to its origin i.e. combustion chamber ( backward facing surfaces). So in theory if all rotating parts would be free to move forward during steadily running engine they wouldn't move. So analogically to center of gravity of an object the central point of thrust within the jet engine lies in geometrical center of backward facing surface of combustion chamber.
