Solar – much too powerful for a pit fiend
Of celestial creatures, the solar is the most powerful. In fact, solars considerably more powerful than a pit fiend. They are CR 23, to the pit fiend’s 20, but more importantly, the solar casts divine spells as a 20th-level cleric. The pit fiend merely gets a number of spell-like abilities – powerful ones, no doubt, but the the sheer magnitude of power that true spellcasting can bring to bear is simply overwhelming. Worse, the solar is too powerful to be affected by the pit fiend’s most powerful non-wish ability – blasphemy. And the pit fiend is not powerful enough to resist a holy word as cast by the solar, which will paralyze, daze, and weaken the pit fiend. The power afforded by wish, of course, is immense, but pit fiends get that only once per year – solars get it once per day.
Planetar – if prepared, can still guarantee victory over a pit fiend
Planetars, a step down in the angelic hierarchy, are perhaps a more reasonable match, though 17th-level cleric spellcasting is still incredibly potent. With a single boost to its caster level, their holy word could daze a pit fiend – though the pit fiend’s blasphemy will do far worse to the planetar. Still, cleric spellcasting is flexible, in ways that the pit fiend’s spell-like abilities are not. The planetar can use those spells to protect himself, ensure he will act first, and so on. A 17th-level cleric can kill a pit fiend, therefore a planetar can.
But it will take very careful leveraging of that 17th-level cleric spellcasting, and the planetar is likely dead if the pit fiend ever gets to act freely, even once; the planetar has only 14 HD, and the pit fiend can get through their 133 HP very quickly if allowed to. One blasphemy is all it would take. The planetar can only win if he is specifically prepared for a pit fiend hunt that day. If a pit fiend simply catches a planetar on the field of battle, the planetar is almost-certainly dead.
Astral Deva – not a prayer
Astral devas, unlike other angels, do not have cleric spellcasting. As such, they lack options that they can attempt to use in response to a pit fiend’s might. A sole astral deva is dead against a pit fiend.
Trumpet Archon or Ghaele – maybe a chance
Trumpet archons, on the other hand, do get cleric spellcasting – 14th-level cleric spellcasting. This puts the trumpet archon at a huge disadvantage against a pit fiend, but cleric spellcasting really is just that good – a very careful, very prepared trumpet archon might be able to take a pit fiend.
This winds up being very similar to the planetar, but with the odds that much further stacked against the celestial, since the trumpet archon lacks 8th- and 9th-level spells.
A ghaele also has 14th-level cleric spellcasting. They’re also even less powerful, in all other ways, than is a trumpet archon. Still, since both are very easily killed by a pit fiend in a single round, their odds are probably pretty similar – that is, almost zero, barring shenanigans with that cleric spellcasting.
Balor – considerably more powerful than pit fiend
Balors are the demonic counterpart of the pit fiend, but like the solar, balors are much more powerful than the pit fiend. Their blasphemy is powerful enough to affect solars, and high-level dominate monster means they can bring in some ridiculous allies. Solars are still considerably stronger, but balors would, at least, give them a fairly hard time.
If a pit fiend leads the forces of Hell, there either must not be any balors available, or some very specific plot explanation would be necessary to explain how a pit fiend manages to push around balors.
Pit Fiend – Mechanically inferior
As indicated above, solars are massively more powerful than pit fiends, and planetars, a step down from solar, could guarantee victory against a pit fiend if sufficiently prepared. For that matter, with enough shenanigans, so too could a trumpet archon or ghaele. On their own side, balors are dramatically more powerful. For a pit fiend to stand up as the leader of Hell, there has to be more to things than their stats. On their stats alone, they simply are not going to win.
The default cosmology gets around this by having pit fiends be smart, ruthless, and organized. They can handle balors, because demons are almost-always solo acts, while the pit fiend has legions behind him. They can beat angels, because angels have scruples, and the pit fiend does not.
In short, pit fiends survive, and even thrive, because pit fiends know all of this. They know they are weaker, in straight combat, than the angels. They also know they’re not going to stand toe-to-toe with a balor and survive. Of the three, they have the fewest innate advantages. And know it.
Therefore, they simply aren’t going to get into that fight. The terrible strength of Hell is in their plans and schemes and betrayals. The pit fiend won’t fight an angel; they’ll corrupt someone. Someone close to the angel, or that the angel will rely on in a crucial moment – and then they will turn on that angel. The pit fiends each have vast forces of devils at their command; the angels are much more the servants of good gods, with only that individual gods’ forces, whatever they are, potentially available to them. The pit fiend will likely get what he wants, but it won’t be through straight combat. That would be much too predictable and much too stupid.
So for your game, assuming you aren’t simply eliminating the balor, solar, and most likely the planetar as well, the pit fiend needs an extra edge. Some reason why he can win, even though the stats say he loses. I recommend the default explanation, personally; make a balor the Dragon to the pit fiend’s BBEG, too proud, quite possibly too crazed, to be an effective leader, and disinterested in the logistics. Make the angels have too many vulnerabilities, too many things they are trying to protect, and too many things they simply will not do, to force the might of solars to be spread too thin to just tromp the forces of hell.
At least one of them, if you consider older edition info
This is partially drawn from some older information, but here you go...
As you stated, the Monster Manual says that Kuo-Toa 'create' gods by believing in them so hard that they manifest. It continues to say this...
While no 5E information exists expanding on this, there is some 3E material that covers this particular goddess.
From the 3rd Edition book Faiths and Pantheons, we have a table on page 221 (list of non-human deities) that has record of Blibdoolpoolp. She is listed as an Intermediate Deity, thus being on the same power level as gods such as Kelemvor, Tymora, Lloth (Lolth), and Helm. She has the Domains of Destruction, Evil, and Water (Pared back to just 'Death' in 5E, see Appendix B of the DMG.)
The 3rd Edition book Player's Guide to Faerun gives us a little more details. On page 53, it introduces her Home Plane: The Fated Depths, which she shared with Sekolah, the god of the Sahuagin.
So, as we can see from here...Blibdoolpoolp is spoken of in the same breath and in the same manner as all other gods. Apart from the fact that she was created by her worshipers believing in her hard enough, she appears to be a fully functional deity.
Now, as for any other gods they may invent...the books are less clear. The phrasing makes it clear that a newly invented god has to reach a critical mass of worshipers before it would be possible for them to actually exist, but specific details are never provided.
Of note, The Fated Depths apparently ceased to exist during the Spellplague. We have no updated information from 4E or 5E on where Blibdoolpoolp presently resides.