One of the ways is using emphatic words (так, просто).. e.g. Я просто устал от этого. Я так устал от этого. - some emphasis will be added, meaning they are a a bit more than tired. Or Я так сильно устал от этого (сильно means 'very much').

Most of the Russian sentences suggested are more formal and might be encountered in literature, except "достало" which is very informal (meaning is close to 'I am pissed off', sometimes might be OK for 'sick and tired', but a bit stronger than that)

I'm sick and tired of being sick and tired. - Я уже просто устал от этой усталости (if used with the right context might sound OK)
I'm sick and tired of this nonsense - Я просто устал от этой ерунды.