Most of the words that are singular after a number are quite old fashioned.
Words like dozen (12), score (20) and gross (144) can be used about anything, and are treated the same as numbers:
- they are singular when preceded by a determiner or a multiplying number
- it is not necessary to use of between a number and the word its refers to
- the plural is only used for approximate numbers.
a dozen eggs
five dozen eggs
dozens of people came to the shop today
For words that have a much more limited usage like head (people and cattle), yoke (oxen) and brace (game birds, but can be used for other things), only rule 1 applies.
a yoke of oxen
five head of cattle
several brace of pheasants
The word pair is widely used in modern english, and this conforms to the normal rules for nouns:
a pair of socks
five pairs of socks
several pairs of socks
For older (imperial) weights, these Ngram graphs for pound and ton show that these units of weight were historically used as a singular after a number, but even a hundred years ago it was a lot more common to use a plural after a number. For stone, the singular and plural are a lot closer, but for ounces, there is no evidence of usage of a singular after a number and for hundredweight instances of the plural are in the minority.
For modern (metric) weights (gram, gramme, kilo, kilogram and tonne), all use a plural after a non-unity number, and also use of.
When an abbreviation is used, whether metric (kg) or imperial (lb), the singular is more frequently used and the of is usually included.
To answer your specific question about litres: Litre (UK)/liter(US) follows the same conventions as other metric units: it uses a plural after a non-unity number and requires of, so the first option is the correct version.
1 - Five liters of water.
You may occasionally see the second option, when the writer wishes to save space.
I think that you are unlikely to see 3 and 4, though you may see the abbreviation
5 l water