逢う is often used for close friends, etc. and may be associated with drama or pathos; 遭う may have an undesirable nuance

to meet; to encounter; to see

Word usually written using kana alone; Esp. 遭う when in kanji

to have an accident; to have a bad experience

出遭う usu. has a negative connotation

to meet (by chance); to come across; to run across; to encounter; to happen upon

出会う／出合う only; Esp. 出合う

to meet (e.g. of rivers, highways, etc.)

出会う／出合う only; Often used imperatively as 出会え

to emerge and engage (an enemy)

meeting; rendezvous; encounter

meeting for the first time; coming across

Esp. 出合い, 出合

confluence

encounter; running into; meeting with (e.g. an accident); being confronted with (e.g. a difficulty)

to experience (something unpleasant); to go through; to suffer

(meeting with) disaster; (having an) accident; mishap; shipwreck; distress

to have an accident; to meet with an accident

to have a bad time; to go through a bitter experience; to get into trouble; to get hurt; to suffer

to go through a bitter experience; to get into trouble; to get hurt; to feel pain

to make (someone) to meet; to let (someone) meet

to expose to; to subject to