Suggested answer:
(1) Only boy and wood are immediately preceded by the indefinite article, e.g.:
A boy from the village was there with a ferret.
But there's a wood just over the top of the hill.

(2) Only boy and wood occur with a plural ending, e.g.:
"You've got two fine boys", I said...
...and then about summer when the woods were green...

(3) Luggage is the only one of the three nouns that only occurs with a singular verb form, e.g.:
Their luggage was being brought down.

However, in some uses wood (with the meaning "The substance making up the central part of the trunk and branches of a tree that can be used by humans to manufacture various items.") cannot take a plural verb form. (See below (4) for examples.)

(4) Boy is a countable noun; it can occur with the indefinite article and it has a plural form followed by a plural verb form, suggesting that boy can be counted. Examples:
"I never had a beard, I'm a boy."
Those two boys are all I've got.

Wood can be both countable and uncountable. It is countable when it occurs with an indefinite article or is in the plural form, e.g.:
...trees into an open place in the middle of a wood.
The woods are perfectly beautiful.

Wood is uncountable when we refer to the hard, fibrous material that is often used as building material. In these cases, wood neither accepts the indefinite article nor a plural form. It also requires a singular verb form, e.g.
...because wood is a material with a visible structure...

Luggage is uncountable as evidenced by the lack of a plural form and also by the fact that it cannot be preceded by the indefinite article, e.g.
...where luggage consists of a couple of new shirts...

Read about articles here (determiners) and about countability here
Terminology: article, countable, definite article, indefinite article, plural, singular, uncountable