Disease itself is very different from sickness or illness. It is usually a specifically diagnosed condition. It could be serious or not. Sickness is a general malady. It could be because of a disease or a temporary upset of the body caused by excessive eating, drinking or some sort of physical activity. Illness describes the way one feels. It means that person is feeling unwell. Illnesses usually imply something is not serious, but is sometimes used to describe a serious condition. To distinguish them, you can see the following sentence. "Her tendency for sea sickness left her feeling ill the entire trip." Here sickness is used to describe a malady caused by the swaying of the ship. But the feeling was described as an illness. Many people also tend to use the word "sick" on the same context as the word "ill". When used in the context of describing the feeling of "unwellness" they are interchangeable. Also, as Alex stated, the word "sick" is generally the only one of the three that is used to express malcontentedness: "I'm sick of your excuses." "His poor attitude makes me sick." It's also used ironically to express something you find exceptional. "That is one sick skateboarding trick." "That new song is really sick."

Disease: Un desorden, enfermedad crónica, algo con lo que naces o adquieres y es difícil o imposible de curar) Illness: Enfermedad, pero es una palabra muy fuerte y 'difícil' de usar, creo que se usa también para decir que alguien tiene una enfermedad grave. Sickness es más usado para describir un sentimiento de enfermedad, hastío, enojo, u otras cosas. Si dices: I feel ill, no suena fluído, es más usado para afirmarlo: I'm ill. Es mejor decir: I feel sick, si quieres expresar que te sientes enfermo, pero si dices 'I'm sick' puede significar muchas cosas dependiendo del contexto, tanto que estas enfermo, como que estás cansado o harto de alguna situación en tu vida (Your attitude makes me sick -> tu actitud me enferma, no te enferma literalmente, sino que te desagrada) Es como yo lo entiendo, sin embargo tal vez sería mejor si tuvieras ayuda de un nativo :)