sonst
otherwise
Introduces a consequence that will occur if a condition is not met. It means 'andernfalls' (otherwise).
Du musst dich beeilen, sonst verpasst du den Bus.
You have to hurry, otherwise you'll miss the bus.

otherwise / else
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otherwise
Introduces a consequence that will occur if a condition is not met. It means 'andernfalls' (otherwise).
Du musst dich beeilen, sonst verpasst du den Bus.
You have to hurry, otherwise you'll miss the bus.

You can recognize the meaning of 'sonst' from the sentence structure. At the beginning of a sentence with the verb in position 2, it means 'otherwise'. In a question, it means 'else' or 'in addition'. After a question word like 'wer' (who) or 'was' (what), it emphasizes that there is no other logical possibility.
Du musst jetzt lernen, sonst schaffst du die Prüfung nicht.
You have to study now, otherwise you won't pass the exam.
When 'sonst' introduces a consequence (otherwise), it often appears as an adverb in position 1 of the sentence. The conjugated verb then moves to position 2, directly after 'sonst'.
Zieh eine Jacke an, sonst erkältest du dich.
Put on a jacket, otherwise you'll catch a cold.
In the meaning of 'normally' or 'usually', 'sonst' often appears in the middle of the sentence to create a contrast between the normal state and a current, different situation.
Heute habe ich ein bisschen Kopfschmerzen, aber sonst bin ich fit.
Today I have a bit of a headache, but otherwise I'm fit.
The question 'Sonst noch etwas?' (Anything else?) is a very common and polite phrase in service situations, for example in a restaurant or shop. It means 'Would you like to order or buy anything else?'.
Das macht dann 5,50 Euro. Darf es sonst noch etwas sein?
That comes to 5.50 euros. Would you like anything else?
In combination with a question word like 'wer' (who), 'was' (what), or 'wo' (where), 'sonst' expresses that the answer to the question is obvious and that there is no other logical alternative.
Natürlich hat er das gewusst. Wer sonst hätte die Antwort kennen sollen?
Of course he knew that. Who else would have known the answer?
also / besides
'sonst' and 'außerdem' can both ask about something additional or mention something additional. You can see this especially in questions like 'Was brauchst du sonst noch?' (What else do you need?). 'außerdem' is used when you add another piece of information or another argument. But 'sonst' also has other important meanings, for example 'otherwise' or 'usually'. For that reason, the words are not always interchangeable. If you simply want to give another argument, 'außerdem' fits better. If you are asking about additional things, 'sonst' can be natural.

Braucht ihr sonst noch etwas für das Frühstück in der Pause?
Do you need anything else for breakfast during the break?
Am Wochenende gehen wir spazieren; außerdem kochen wir etwas Gesundes mit einem Freund.
At the weekend we're going for a walk; besides, we're cooking something healthy with a friend.