I know that Rakshasa can't be affected by spells of 6th level or lower ... but does that apply to spell with verbal components, or in a case where it does thunder damage?
The Rakshasa stat block has this property:
Limited Magic Immunity. The rakshasa is immune to spells of 6th level or lower unless it wishes to be affected. It has the advantage of saving throws against all other spells and magical effects.
The spell Silence is written like this:
2nd-level illusion (ritual)
Since Silence is a 2nd level spell, so the Rakshasa is immune to its effects.
The Rakshasa is immune to the spell, therefore, he can still use spells with verbal components, speak and do anything to make sound, including thunder. However, the spell silence states:
Any creature or object entirely inside the sphere is immune to thunder damage,
The creature itself is affected not the Rakshasa, so the Rakshasa can cast a spell with thunder damage, but any creature within the sphere of silence is immune to the damage and so will not take the damage.
Silence would impede a Rakshasa
Let's go through the effects of the spell:
For the duration, no sound can be created within or pass through a 20-foot-radius sphere centered on a point you choose within range. (PHB 278)
This effect does not target any creatures at all. It targets the area itself. A Rakshasa cannot talk or hear through it anymore than it could see through a wall of stone or breathe in a tank filled by create/destroy water.
Any creature or object entirely inside the sphere is immune to thunder damage, and creatures are deafened while entirely inside it.
Now this effect does target creatures. While the fiend could choose to be immune and thus would not be deafened (or immune to thunder damage), there is still no sound to be heard really. The most it could hear is its tummy rumbling.
Casting a spell that includes a verbal component is impossible there.
This is also an environmental effect. It is a product of there being no sound in the area, as we can see in the general rules of such components:
a character who is gagged or in an area of silence, such as one created by the silence spell, can't cast a spell with a verbal component. (PHB 203)
The last sentence of the spell is just a clarification, a reiteration of a general rule. Thus it is like the first effect, and would also affect a Rakshasa.
I think it's simple enough.
For the duration, no sound can be created within or pass through a 20-foot-radius sphere centered on a point you choose within range.
No sound can be created means the air within this area is not reacting to, therefore not transferring vibrations -> sound. This spell clearly affects the air within the area, which probably cannot be immune to it. It does not matter if a Rakshasa is immune to silence. It won't be deafened or silenced, but still It could not hear anything, because air itself stays still, and cannot make any sound for same reason, therefore cannot cast spells that include verbal component. Air is affected inside the area, not the Rakshasha. ... I know DnD is not a physics simulator :) that's why it has rules. To clearly state how it differs from real life and real life physics. Otherwise we could just state anything that's not among the rules. We could just say that in DnD if you stand on your hands then spit over water it starts burning and creates red smoke. Then one would argue that's not in the rules, another would simply say, well it's not a physics simulator. :) So the question is, is there a rule that says sound travels differently in DnD air, than air IRL. I can accept that the incantation of a verbal component does not need to reach anyone, it just had to be said, then ok, the Rakshasa can cast spells. It just won't be heard if it was casted inside the silenced sphere, and of course it would not have an effect, if for the effect it has to be heard by the targets.