Experience, undergo, sustain, suffer are comparable when they mean to pass through the process of actually coming to know or to feel.
Experience means little more than this. It implies that something (as a sensation, an emotion, or an occasion) is known not from hearsay but from an actual living through it or going through it.
Undergo carries a strong implication of bearing or enduring or of being subjected to that is almost lacking in experience; it frequently takes as an object a distressing experience (as pain, suffering, or hardships) when the subject names a person.
But when it is used with objects which represent a process which covers years or ages of time, it comes closer to experience in meaning, though it seldom takes an individual as its subject. Very occasionally, when the idea of submission to or imposition upon is stressed, the subject of undergo in the active voice may be impersonal.
Sustain suggests undergoing infliction or imposition without implying as a necessary concomitant courage in resisting or enduring.
Suffer, which is frequently used interchangeably with sustain in this sense, carries a more marked implication of the harm done or injury wrought and is preferable when what is affected is a thing; moreover, suffer may also be used intransitively.
Sometimes suffer loses its distinctive quality and is then nearly equal to experience.