Learn Swedish: Plötsligt kom ovädret och vi kunde inte grilla. - Suddenly the storm came and we could not grill.

skulle inte grilla means "we weren't going to grill" (a lack of intention). Because the storm ruined a plan you already had, you use kunde inte grilla to mean "we could not grill" (a lack of ability). Both use a past-tense modal verb plus a bare infinitive.

Why is the word order kom ovädret and not ovädret kom?

Swedish uses the V2 (verb-second) rule. Because the sentence starts with the adverb Plötsligt (Suddenly), the verb kom must be in the second position. This forces the subject ovädret to move right after the verb.

How does the word ovädret mean "the storm"?

It is built from the prefix o- (which often means "un-" or "bad") and the noun väder (weather). So ett oväder is "bad weather" or a storm. The -et suffix makes it definite: ovädret (the storm).

Why is grilla in the infinitive form here?

Just like in English, Swedish modal verbs like kunde (could) are followed by a bare infinitive (the infinitive form without the word att in front of it).