Reality check won't be kind to this idea.
The short version is that your planet killer requires handwavium and lots of it.
the Earth is taken over and literally eaten by a race of giant alien beings who use mass-energy conversions to power themselves (These guys are as big as the sun, body structure of StarCraft Leviathans, sentient)
First things first, anything that big will likely become a Sun. That is to say it is unavoidable that gravitational forces will result in it becoming a more compact body. If there is enough mass it will result in fusion taking place in the core. The physics for this (and you wanted a reality check) is absolutely unavoidable.
So they can't exist.
Note that the leap from these Leviathan's (about $7$ km in size) to something Sun sized (a little short of $700,000$ km in radius) is vast. An object 7km in radius which was hollow with a shell $0.5$ km thick made of something the density of water would have a mass of about $2.9\times 10^{14}$ kg. An object as large as the Sun with a similar shell would have a mass of about $3\times 10^{24}$ kg, which is about half the mass of the Earth ! And that's for an empty (!) entity as you describe it. It would end up as a planet - there's no practical way around this.
Now, the aliens have discovered machine augmentation. They lack limbs, but instead use long tentacles as graspers.
Interacting with other objects when you're planet size or larger in mass means they collide with you with enormous force - you have a gravitational field that attracts objects.
So what this object will have is lots of craters, like our moon (and the Earth would have them if it didn't have weathering and geological activity that smooths out the wrinkles over times).
Without a home, humanity takes it upon itself to do the impossible: colonise the bodies of the beasts themselves.
Well they'll be planets, so that seems quite reasonable.
It also means that on approaching an Earth sized body the two large masses will start accelerating towards one another and the collision will be enormous and destroy both (in the sense of creating enough heat to melt both and they would reform as one or more bodies).
They suck material from heavenly bodies through a toothless mouth,
You cannot suck something in a vacuum. There's nothing to suck. You can't create an inflow of gases by sucking which would drag other things with it.
and their stomach functions as a mass-energy reactor, with the aid of a particle-accelerator type environment,
Particle accelerators are enormous power drains - they could not be used to generate more power than they consume.
A mass-energy reactor is just buzz-words. It's meaningless.
If you mean they convert mass to energy, then that's fission or fusion.
where they collide the particles and utilise the Hawking radiation to power themselves.
You clearly don't know what Hawking radiation is (more buzz words being slapped together). It's a very small and very theoretical radiation expected in the region of black holes. It's not going to happen in any other circumstances and it requires an enormous gravitational field to power it. It's not possible to use Hawking radiation in any way you're suggesting.
The plan of the protagonists is to enter using special drop pods along with the material, latch onto the oesophagus wall, burrow into the muscle and deploy a colony there. The damage will be smalller than a pinprick for the giants, and they won't even notice. However, the immune system will.
All of this makes no sense.
An immune system would not react to anything unless it did something to activate it. Just being present is not enough. Humans could, in fact, probably live on the surface of your planet mass object. Going inside is pointless.
So, my question, what kind of punches would the immune system, biological or semi-mechanical, have to pack to present an actual threat to the human drop pods or the people themselves?
The entity could safely ignore the humans and they could exist together without issue.
The aliens do generate their own gravitational field.
Unavoidable with the mass of a planet or star.
Humanity's technological level is sufficient to allow interplanetary travel.
Which begs the question why are we staying near this planet killer ?
More to the point, if you can travel between stars it beggars the imagination you couldn't have just fired an extremely high kinetic energy lump of matter at the planet killer in the first place. At minimum a deterrent, at best enough to do it serious damage.
The immune system cells of the giants are likely to be bigger than the people or their drop pods.
Even if I accept the need for such things (which I don't) they are grenade fodder. A non problem.
The humans are carrying a military force, including heavy artillery, armored vehicles, and troop transports
Precisely what these idiots could do against a planet sized mass is beyond me. Every nuke on Earth would do no damage at all in any practical sense to something as large as you describe. I would describe them as wasted effort. There's no need or purpose in entering the body of the planet killer at all and there's no need to worry about an immune system that won't care what these things do.