Odor foedus puellam terret.

We know from the case endings, not mainly from word order.

• odor is the subject: it is in the nominative singular
• puellam is the direct object: the ending -am marks it as accusative singular
• terret is he/she/it frightens

So the sentence means that the foul odor frightens the girl, not the other way around.

Because puellam is the accusative singular form of puella.

For a regular first-declension noun like puella:

• nominative singular: puella
• accusative singular: puellam

Latin uses the accusative for the direct object, the person or thing directly affected by the verb. Since the girl is the one being frightened, Latin uses puellam.

Foedus describes odor.

You can tell because foedus is:

• masculine
• singular
• nominative

and it matches odor, which is also masculine singular nominative.

It does not describe puellam, because puellam is feminine accusative singular. If the adjective described puellam, it would need to be foedam, not foedus.

Because odor is masculine, not neuter.

The adjective foedus, foeda, foedum changes form to agree with the noun it modifies:

• masculine: foedus
• feminine: foeda
• neuter: foedum

Since odor is a masculine noun, the adjective must also be masculine: foedus.

Latin word order is much more flexible than English word order.

An adjective can come:

• before the noun
• after the noun
• sometimes even separated from the noun

So odor foedus is perfectly normal Latin. The endings show that the two words belong together, even though Latin does not have to place the adjective before the noun the way English usually does.

Terret is:

• 3rd person singular
• present tense
• active voice
• indicative mood

It comes from the verb terreō, terrēre, meaning frighten or terrify.

The ending -t tells you it means he/she/it frightens. Here the it is the odor.

Because Latin does not have articles like English the and a/an.

So a noun like odor can mean:

• an odor
• the odor
• sometimes just odor in a general sense

Likewise puellam can mean:

• a girl
• the girl

The context or the translation chosen in your textbook tells you which is most natural in English.

Yes, often they could.

Because Latin uses case endings, the basic meaning usually stays the same even if the order changes. For example, these would still mean essentially the same thing:

• Puellam odor foedus terret.
• Foedus odor puellam terret.
• Puellam terret odor foedus.

What changes is usually the emphasis, not the core meaning.

That said, the original order is very natural Latin: the verb terret comes at the end, which is common.

Here it is the adjective meaning foul, hideous, or disgusting.

There is also a different Latin word:

• foedus, foederis = treaty, alliance, compact

That is a noun, not an adjective. In this sentence, foedus clearly works as an adjective because it agrees with odor.

Here is the grammatical breakdown:

• odor: a 3rd-declension masculine noun
• foedus: a 1st/2nd-declension adjective
• puellam: from puella, a 1st-declension noun
• terret: from terreō, a 2nd-conjugation verb

This is a very typical beginner-level Latin sentence because it lets you practice:

• subject in the nominative
• direct object in the accusative
• adjective agreement
• a present-tense verb

In a common restored Classical pronunciation, you could say it roughly like this:

OH-dor FOI-dus pu-EL-lam TER-ret

A few helpful points:

• oe in foedus is pronounced like oi in oil
• puellam has the stress on EL
• terret has a clearly pronounced rr

Pronunciation traditions differ somewhat, but those points are a good start.