I told him no right off the bat...But he's extremely insistent about
Just tell the player "no," again; you are allowed to do that as DM
There are a number of reasons for this.
An invisible stalker is an elemental; PCs are humanoids1
The CR of an invisible stalker is 6; it usually takes 2 or 3 PCs of
level 6 to defeat an invisible stalker; the ...
Ask the player "why?"
First step to solving these types of issues is asking why they want a thing. If the character wants to be invisible all the time just for the sake of that, just say no. If they like the idea of being able to attack from being hidden or that type of thing then you can help them out.
The Gloomstalker Ranger is invisible in darkness to ...
This is likely unbalanced
For your tiefling paladin, this is likely at least a +3 to AC, which, depending on their build, could give them 21 AC at level 4 (shield + chain mail from Paladin starting gear, +3 base CHA modifier.) This is quite powerful relative to other options, and will improve with any additional ASI.
If this doesn't look that powerful to ...
The Bad News
As others have pointed out, Invisible Stalker is a monster and the stat block it uses is just not viable for a PC. You could always start tweaking the different parts of it to try to get something balanced but chances are it would never really pan out and your player would still be far too strong, or so saddled with drawbacks that he can't have ...
No, not in the slightest
You're trying to make a D&D 5e character, and you want to play:
A half dwarf / half giant
This is not something that exists in D&D 5e by default, so you'd have to homebrew it
who dual-wields giant-sized axes
also not allowed, you can't dual wield two-handed weapons in 5e
attached to magic item chains that leave his ...
Some of this is do-able in 5e, but some is not.
If I understand your question correctly, you're asking if this highly specific character build can be made in D&D 5th edition.
Some of this is possible, and your DM wil probably grant most requests:
Backstory details are entirely fine in 5th edition.
The Fullangr doesn't exist in D&D 5e, but ...
One thought, allow them to be invisible, but at a low level they have not ability to interact with the world around them while invisible. For instance, they can walk though doors and walls,but cannot open doors. They can view everything around them, but cannot pick up things.
This forces them to come out of invisibility then once fully visible (whole) they ...