Which nouns have irregular plurals from different words?

Just a few.

I can remember only ребенок - дети (child - children).

There are some nouns that have two or more plurals, one of which is derived from a totally different word.

год (year)

The singular is год (year) and the plurals are го́ды and лета́ (years)

Examples:

Ему́ два́дцать оди́н год. — He is 21 years old.
Ему́ два́дцать два го́да. — He is 22 years old.
Ему́ два́дцать пять лет. — He is 25 years old.
Сколько тебе лет? — How old are you? (literally: How many years to you?)

You should use the appropriate case of год after simple or compound numbers ending in один (1), два (2), три (3), or четыре (4), except for 11, 12, 13 and 14 (and 111 - 114, 211 - 214 etc.) - for these and all other numbers, and with adverbs of quantity (много, сколько, etc.), use the appropriate case of лето. (source: wiktionary)

ребёнок (child)

The singular is ребёнок and the plurals are дети (children), ребята (guys) or dual form ребёнка (used with the numbers два, три, четыре)

Use дети as the usual plural for children.
Use ребята when the meaning is Guys!, Boys!, Fellows!
With the numbers 2,3,4 the following dual form is possible: два ребёнка, три ребёнка, четыре ребёнка (the dual form = Genitive singular).

Examples:

В комнате один ребёнок. — There is one child in the room.
У вас есть дети? — Do you have children?
Сколько у тебя детей? — How many children do you have?
У меня двое детей. — I have two children. (see Collective numbers)
У меня трое детей. — I have three children.
У меня четверо детей. — I have four children.
У меня пять/пятеро детей. — I have five children.
У меня семь/семеро детей. — I have seven children.
У меня два/три/четыре ребёнка. — I have two/three/four children. (Dual grammatical number)
Я не знаю этих ребят. — I don't know these guys/boys.