The words inveighed, invade sound the same but have different meanings and spellings. Why do inveighed, invade sound the same even though they are completely different words?
The answer is simple: inveighed, invade are homophones of the English language.
To enter by force in order to conquer or pillage.
To encroach or intrude on; violate: "The principal of the trusts could not be invaded without trustee approval” ( Barbara Goldsmith).
To overrun as if by invading; infest: "About 1917 the shipworm invaded the harbor of San Francisco” ( Rachel Carson).
To enter and permeate, especially harmfully.
Simple past tense and past participle of inveigh.
Definitions from The American Heritage® Dictionary of the English Language, 4th Edition, from Wiktionary, Creative Commons Attribution/Share-Alike License and Wordnik.
Homophones (literally "same sound") are usually defined as words that share the same pronunciation, regardless of how they are spelled.