La inventaro enhavas ĉiun meblon.

La is the definite article, so la inventaro means the inventory: a specific inventory already known from the context.

Esperanto has:

• la = the
• no word for a/an

So:

• inventaro = inventory / an inventory
• la inventaro = the inventory

In this sentence, the speaker is talking about a particular inventory, not inventories in general.

Enhavi means to contain or to include.
So enhavas means contains.

That fits inventory better than plain havas:

• havi = to have
• enhavi = to contain

So:

• La inventaro havas... would sound more like The inventory has...
• La inventaro enhavas... more naturally means The inventory contains...

The prefix en- often adds the idea of in or inside.

Because ĉiun is the accusative form.

In Esperanto, the direct object usually takes -n.
Here, ĉiun meblon is the direct object of enhavas, so ĉiu becomes ĉiun.

Compare:

• Ĉiu meblo kostas multe. = Every piece of furniture costs a lot.
  
  • here it is the subject, so no -n
• Mi vidas ĉiun meblon. = I see every piece of furniture.
  
  • here it is the object, so it takes -n

Because meblon is also part of the direct object.

In Esperanto, when a noun is in the accusative, words that go with it also agree with it. So both the determiner and the noun show the accusative:

• ĉiu meblo = every piece of furniture
• ĉiun meblon = every piece of furniture (as object)

So:

• ĉiu → ĉiun
• meblo → meblon

This matching is very common in Esperanto.

That is a very common question. Esperanto meblo means a piece of furniture or a furniture item, so it is a countable noun.

Examples:

• meblo = a piece of furniture
• mebloj = furniture items / pieces of furniture

So ĉiun meblon literally means every furniture item or every piece of furniture.

English uses furniture as an uncountable noun, but Esperanto often prefers a countable noun here.

Yes, but it is not exactly the same emphasis.

• ĉiun meblon = every piece of furniture, focusing on each item individually
• ĉiujn meblojn = all the pieces of furniture, focusing more on the whole group

Both can be correct depending on what you want to stress, but ĉiun meblon is a very natural way to say every piece of furniture.

Because ĉiun already works as the determiner.

In Esperanto, you do not normally stack la together with ĉiu in this kind of phrase. So you say:

• ĉiu meblo
• ĉiun meblon

not:

• la ĉiu meblo
• la ĉiun meblon

Ĉiu already tells you how the noun is being limited: each/every.

Yes. Esperanto word order is fairly flexible because the accusative -n shows what the object is.

The normal, neutral order is:

• La inventaro enhavas ĉiun meblon.

But other orders are possible for emphasis, for example:

• Ĉiun meblon enhavas la inventaro.

That is still grammatical, because ĉiun meblon clearly has the object marking -n.
Still, for ordinary prose, the original order is the most natural.

Usually either translation works.

Ĉiu can often mean:

• each
• every

In this sentence, ĉiun meblon can be understood as:

• each piece of furniture
• every piece of furniture

English chooses between each and every based on style and nuance, but Esperanto ĉiu covers both very naturally here.