"Euch" is the accusative form of "ihr". When the pronoun is the subject of the sentence, use the nominative case "ihr", e.g. Ihr habt Bücher "You (pl.) have books." When the pronoun is the object of the sentence, use the accusative "euch", e.g. Sie mag euch "She likes you (pl.)."
In terms of "du", the nominative case is "du" and the accusative is "dich". The uses of these are the same as "ihr" and "euch", but mean "you" in the singular, informal sense.
Hope this helps!
du = you singular informal in nominative (i.e. subject position)
ihr can have different meanings depending on whether it is used as personal pronoun or possesive pronoun:
ihr = you plural informal in nominative (i.e. subject position)
ihr = her (possessive* or dative)
ihre = their (possessive)*
Ihr (with capital) = your (possessive, singular or plural) formal*
(*) these are inflected according to the noun they are applied to.
Y'all hasn't been lost; it is a relatively modern invention. Originally English had 'thou' as the 2nd person singular pronoun, and 'ye' as the 2nd person plural pronoun. 'Thou' was informal, familiar, just like 'du' in German (you can see the similarity). It even has similar conjugations: Thou hast – Du hast; Thou goest – Du gehst. Not surprising since they have the same origin.
Later the plural 'ye' started to be used as a formal, respectful way of addressing people, also in the singular, and it changed to 'you'. Now 'thou' has almost disappeared except in some dialects, and therefore the distinction between singular and plural 'you' has also disappeared. In some regions they try to compensate this with inventions like y'all, you all, etc. I wonder why not the original 'ye'? :)