孤 =(alone);单 = (single)
孤单 = alone/ solitary
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孤=(alone); 独 = (single/alone)
孤独 = alone/ solitary/ unsociable
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寂 = quiet; 寞 = deserted
寂寞 = lonely; loneliness
孤单 mainly describes a physical state of being alone. It can be used to describe a feeling of loneliness, as in "感到孤单" (feel alone = lonely)
孤独 also describes a physical physical state of being alone. It can be used to describe a feeling of loneliness, as in "感到孤独" (feel alone = lonely), It can also be used to describe a personality, as in "他性恪很孤独" (he is very unsociable) - You cannot say "他性恪很孤单"
寂寞 is mostly an emotion or feeling. You can be surrounded by friends and still feel lonely. For example: "無敵是最寂寞" (unrivaled people are the most lonely people)
People do not physically being 寂寞; being physically 孤单/孤独 (alone) can make you feel 寂寞, but being 寂寞 (lonely) doesn't require being alone
Actually, feeling 孤单/孤独 (feel alone = lonely) doesn't require physically being alone