All of these verbs have (in a wider or narrower meaning) a result, that is relevant. The result might be a state, an object or something else. [This is probably not the ethymological root, but it works.]
Example verb → the relevant result → meaning of the verb
erkennen → image/knowledge → realize something / make out something
erzählen → story → tell a story
erkaufen → loss of currency → buy something by paying a currency
erhalten → conservation of a state → to conserve a state
erstellen → existencs of something → create something
erfahren → knowledge/experience → experience sth/get to know sth
erlösen → relevation of something painful → relieve of something painful
erledigen → state of getting rid of → get rid of something
erinnern → state of having in mind → remember (=sich erinnern) or remind (jemanden erinnern)
erwachen → awakenness → awaken
erliegen → defeat → getting defeated by something
ermüden → tiredness → get tired
erröten → red face → getting red in the face
erwärmen → warmness → getting warm
erzittern → state of shaking → shake/shaken
erdenken → thought → create a thought
erblühen → blossom → blossum
erglühen → red heat → to heat something to red heat (?correct english?)
erklingen → sound → to create a sound
erfragen → answer → to ask (a specific question)
erdrücken → result of pressure e.g. collapse/death → to pressure something to death / to collapse
ermorden → death → murder
ertrinken → death → drown (by oneself)
ertränken → death → drown somebody else / some living thing
ersticken → death → choke somebody / oneself to death
erstechen → death → stab somebody to death
For some verbs, the difference between the version with and without the prefix "er-" is the importance of the result:
erkaufen: The loss of some currency (not necessarily monetary) is important.
kaufen: Something is bought. The loss of the currency is not important.
Example: Er erkauft sich Erfolg durch weniger Freizeit. = He's "buying" success by "paying" with spare time.
erfragen: The result is important, which means, someone's asking for something specific.
fragen: to ask, perhaps specifically, perhaps unspecifically.
Example: Er fragt nach dem Weg zur Bahnhof. = Er erfragt den Weg zum Bahnhof. = He's asking for the way to the station.
Example: Er fragt den Deutschlehrer. = He's asking the German teacher. BUT: Er erfagt den Deutschlehrer. = He's asking, who his German teacher is.
Of course, if you ask something, you want to get an answer. But there are other aspects of asking (who, when, where, for what reason). The verb "fragen" is used for any of these aspects. The verb "erfragen" is used, if the result is of specific importance.