I noticed this old comment on Legends of Localization:

Challenge accepted! (The part about giving a correct explanation, anyway. Explaining it in a way that makes sense to a non-native speaker is well beyond me.)

The main problem is agreement. English requires that you specify whether nouns are singular or plural. This is known as Number, which I’ll capitalize for clarity. Whichever they are, English also requires that certain related words (determiners, pronouns, and verbs) must be inflected to agree with the Number.

Let’s start with the subject, the noun phrase All your base. All and your are determiners. Some determiners must modify a singular or plural noun for agreement. Both your brother is ungrammatical, as is each your brothers. Base is a singular noun but all is a plural determiner, so these don’t agree. It should be All your bases.

…But what about these examples?

In both of these examples, all is used with a singular noun. What gives?

In the first example, the difference is that team can be used as a collective noun. Collective nouns can be treated as plural or singular for notional agreement, depending on what the speaker is trying to imply. Base is not a collective noun¹, so it doesn’t qualify for this exception.

In the second example, all has more than one definition. One means every one of. The other means the entirety of. Which definition is intended is inferred based on the Number of the modified noun. All your hearts means that there are multiple hearts, and we’re talking about every one of them. All your heart means your whole heart.

All your base could be grammatical, if the text meant to say, Your entire base belongs to us. If it’s instead saying, Every one of your bases has been taken, it would be ungrammatical.

The same issue is in the original Japanese, which doesn’t require specifying Number. 全て (subete) means, just as in English, both every one of and the whole of. But it’s more likely intending multiple bases. The villain says that they’ve gotten help from the army of the federation government, which suggests a large operation.

On to the verb phrase are belong. There are two issues here. One is agreement again. Base is singular, so the verb must be inflected accordingly. Base belongs but bases belong. If there’s an auxiliary verb, the auxiliary verb might need to be inflected instead. For example, if the auxiliary verb were do, then bases do belong or base does belong would be correct. Are is inflected as if the subject, base, were plural. Base are is ungrammatical. It must be bases are or base is.

More importantly, are can’t be used as the auxiliary verb here.

Auxiliary verbs in English include have, do, is, can, will, need, ought, must, and maaaaaaybe to².

The copula (be) as an auxiliary verb has a couple of uses. One is to facilitate a passive construction. All your bases were taken over by CATS could be a grammatical example. Belong is an intransitive verb, so it can’t be used in a normal passive construction.³ The passive also requires the accompanying verb to be inflected as a past participle (i.e. belonged instead of belong).

Another use is to facilitate continuous aspect. E.g. He is running. This requires the accompanying verb to be inflected as a present participle (i.e. belonging instead of belong). Belong is a stative verb and can’t take a continuous aspect at all. It is belonging to him is ungrammatical.

So the are in All your base are belong to us only serves to make it more ungrammatical.

There’s an important seeming exception to clear up. What about I am become death, destroyer of worlds? Here the copula is used as an auxiliary verb that’s neither passive nor continuous. Why can’t bases are belong follow the same construction?

I am become death is not grammatical in modern English. People recognize what it means because it’s grammatical in Early Modern English. Using this construction sounds antiquated or poetic, similar to using words like thou and hath. You probably wouldn’t hear it in a science fiction setting about colonies in space.

This function has been taken over by the auxiliary verb have in modern English. I am become death means I have become death. He is risen means He has risen. The king is arrived means The king has arrived. And so on. To know whether such a construction could be grammatical in older variants of English, try substituting the word have. All your base have belong to us is still ungrammatical.

Fixing the agreement and verb inflection, All your bases have belonged to us would be grammatical, but it wouldn’t make sense in context. That wouldn’t be a revelation that they’ve suddenly taken over the bases; it would instead mean that they’ve secretly owned them the whole time.

No matter what exceptions, interpretations, or oddities you consider, there is no way to salvage All your base are belong to us. Which leads to the question, Why is it funny?

I suspect it’s because humor involves subverting expectations. Like that old Emo Philips joke: I find humor in taking ordinary things and turning them upside down. For example, a small child. Grammar gives us expectations about what people will say next. Ungrammaticality is a surprise, and sometimes that’s all humor needs.