In B/X, ALL elves and dwarves speak six languages each. It is one language more than the smartest human wizard (well, unless you're using something like Old School Feats to become a linguist...).
Is EVERY dwarf a polyglot? This doesn't make sense...
What if these are similar dialects? Dwarves speak "Dwarvish, Gnomish, Goblin, Kobold". You can see dwarves and gnomes (their cousins) sharing a language, right? What if goblins and kobolds learned with them? This is the language of the (short) underground people.
What about elves? They speak "Elvish, Gnoll, Hobgoblin, Orcish". Sounds strange, since those are monsters in B/X terms.
Orcs are "ugly, bad-tempered, animalistic humanoids who live underground and are active at night. Sadistic bullies who hate other living creatures and delight in killing." in the OSE SRD.
Hobgoblins are "Larger and nastier relatives of goblins. Dwell underground, but commonly seek prey above ground.".
And gnolls are "Lazy, humanoid hyenas of low intelligence that live by intimidation and theft. Legends say that gnolls were magically created by a wizard who crossbred gnomes and trolls."
Now, this doesn't make ANY sense...
Unless short species have tighter social connection than taller species. Which sounds a bit ludicrous.
Or, we can rationalize it saying that gnolls, hobgoblins and orcs spent their waking hours outside... only sleeping in caves, etc. Or that orcs are warped elves (as in Tolkien). And trolls are related to elves somehow (as in Poul Anderson). And hobgloblins are... well, a mix of elves and goblins?
But it is all a bit unintuitive and forced.
And I didn't even mention alignment languages until now.
Languages in B/X is one of those idiosyncrasies - like immunity to ghoul paralysis - that works in Basic (there are few monsters, you can speak with some of them), barely works in Expert (now there are more than a hundred monsters) and break if you're expanding the game even further.
You can handwave it, use it as written, or ignore it altogether (as I've seem frequently).
However, having coherent languages improves immensely on world-building... as everyone who read Tolkien knows.
Dark Fantasy Basic tries to make some sense of language - including alignment languages, "common" and dialects. You can read the whole thing here. It doesn't deal with demi-human languages, however.
Well, my next book is likely to be about demi-humans... And I'm wondering if it should include some ideas on languages. For now, I think I'd just say that elves and dwarves speak only three languages by default - and the last three languages on either list can only be picked by high-Intelligence characters.
And "cousin" languages can communicate, albeit with some difficulty: dwarf/gnome, goblin/hobgoblin, and maybe even elf/orc... depending on your setting.