Ο εμβολιασμός, η στείρωση και η αποπαρασίτωση έγιναν χτες.

Because each noun has its own grammatical gender, and the definite article has to agree with it.

• ο εμβολιασμός = masculine
• η στείρωση = feminine
• η αποπαρασίτωση = feminine

This is about grammar, not biological sex or “natural” gender. In Greek, nouns simply belong to gender classes.

A useful pattern:

• nouns ending in -μός are often masculine
• nouns ending in -ση or -ωση are often feminine

So the articles are changing to match the nouns.

Because the subject is actually a list of three things joined by και:

• ο εμβολιασμός
• η στείρωση
• η αποπαρασίτωση

Together, they make a plural subject, so the verb is plural:

• έγιναν = they happened / they were done

This works just like English:

• The vaccination, the sterilization, and the deworming were done yesterday.

Not was done, but were done.

Έγιναν is the 3rd person plural aorist form of γίνομαι.

Dictionary form:

• γίνομαι = to become, to happen, to take place

In this sentence, it does not mean became.
Here it means something like:

• happened
• took place
• were carried out
• were done

So έγιναν χτες means they were done yesterday or they took place yesterday.

Because γίνομαι is very natural in Greek for events, procedures, and actions that take place or get done.

So Greek often says something like:

• Η επέμβαση έγινε χτες. = The operation was done yesterday.

This sounds natural in Greek, even though English may prefer was done.

If you used κάνω, the sentence structure would usually be different, because κάνω normally needs someone who does the action:

• Ο γιατρός έκανε τη στείρωση χτες. = The doctor performed the sterilization yesterday.

So:

• γίνομαι focuses on the event/procedure happening
• κάνω focuses on the person doing it

They are in the nominative case, because they are the subject of the sentence.

You can tell from the articles too:

• ο = nominative masculine singular
• η = nominative feminine singular

So:

• ο εμβολιασμός
• η στείρωση
• η αποπαρασίτωση

are all nominative subjects, and the verb agrees with them as a combined plural subject.

Greek very often uses the definite article where English might or might not.

Here, the article before each item makes the list sound definite and complete:

• ο εμβολιασμός, η στείρωση και η αποπαρασίτωση

This is like saying:

• the vaccination, the sterilization, and the deworming

Repeating the article in a list is very common and natural in Greek.

If you removed the articles, the sentence would sound less natural in this context, especially if you are talking about specific procedures that were carried out.

Yes, it can go somewhere else. Greek word order is more flexible than English.

Here:

• Ο εμβολιασμός, η στείρωση και η αποπαρασίτωση έγιναν χτες.

Putting χτες at the end is completely natural and neutral.

You could also say:

• Χτες έγιναν ο εμβολιασμός, η στείρωση και η αποπαρασίτωση.

That gives a little more emphasis to yesterday.

So the end position is normal, but not the only possibility.

Yes. They both mean yesterday.

• χτες is a very common modern spoken form
• χθες is the more traditional spelling

In everyday Greek, χτες is extremely common and natural.

So if you see either one, the meaning is the same:

• χτες = χθες = yesterday

Because Greek punctuation in lists works much like English punctuation.

In a simple list:

• items are separated by commas
• normally there is no comma before και

So:

• Ο εμβολιασμός, η στείρωση και η αποπαρασίτωση...

This is the normal Greek way to write:

• the vaccination, the sterilization and the deworming...

A comma before και is usually not needed here.

Yes. Depending on context, στείρωση can mean:

• sterilization in a general sense
• spaying/neutering in an animal or veterinary context

So if this sentence is about a pet, η στείρωση would very naturally be understood as the spaying/neutering.

Greek often uses one word where English may choose a more specific term based on context.

A rough guide:

• ο εμβολιασμός → em-vo-liaz-MOS
• η στείρωση → STI-ro-see
• η αποπαρασίτωση → a-po-pa-ra-SEE-to-see
• έγιναν → E-yi-nan
• χτες → htes

A few helpful notes:

• στ sounds like st
• γι in έγιναν sounds like a soft yi
• the stressed syllable is marked by the accent:
  • εμβολιασμός
  • στείρωση
  • αποπαρασίτωση
  • έγιναν

The accent mark is important in Greek because it shows where the stress goes.

If you were talking about just one procedure, the verb would be singular:

• Ο εμβολιασμός έγινε χτες. = The vaccination was done yesterday.

• Η στείρωση έγινε χτες. = The sterilization / spaying was done yesterday.

• Η αποπαρασίτωση έγινε χτες. = The deworming was done yesterday.

So:

• έγινε = singular
• έγιναν = plural

That contrast is very useful to notice.