Learn Finnish: Meillä on tänään paljon sikoja.

You are thinking of the nominative plural siat (pigs), which drops the k (weak grade) because the -t ending closes the syllable. However, the partitive plural ending -ja does not close the syllable. Because the syllable remains open, sikoja uses the strong grade and keeps the k.

Where did the o in sikoja come from? The word for pig is sika.

This happens because of a rule for forming plural stems. In two-syllable words ending in a, if the first vowel is i, e, or a, the final a changes to o before adding plural endings. Here, the stem sika- becomes siko-, to which we add the plural marker i and the partitive ending a (which blend together to form -ja).

Why is sikoja in the partitive plural?

The word paljon (a lot) always requires the word following it to be in the partitive case. Because pigs are countable objects and there are many of them, we must use the partitive plural form sikoja rather than the singular.

Why does the sentence use on (is) if there are multiple pigs? Shouldn't it be plural?