Learn Portuguese (Portugal): Tu disseste que o barulho aconteceu à noite. - You said that the noise happened at night.

Dizer (to say/tell) is an irregular verb in the simple past tense (Pretérito Perfeito). Instead of using the normal stem, it changes to diss-. For the tu (informal "you") form, you add the ending -este, making it disseste.

Do I always need to include que here, or can I leave it out like we often do in English?

Unlike in English, where you can easily say "You said the noise happened" (dropping the word "that"), in Portuguese you cannot skip it. You must always use que to connect the two halves of the sentence (Tu disseste que...).

Is aconteceu also an irregular past tense verb like disseste?

No, aconteceu (happened) is completely regular. It comes from the verb acontecer (to happen). Because o barulho (the noise) acts as a singular "it", we use the regular third-person ending for -er verbs in the past tense, which is -eu.

Why does the "a" in à noite have a backward accent mark?