What exactly is the difference between やめろい and やめろ?
Is this い the same as the one used to strenghten assertions and statements like the い used in the sentence-final かい, だい, and がい? Can it be used with every other verb in its imperative form?
Lastly, is this やめろい common at all? I assume it's a little less common than やめろ since it probably sounds quite rude.
Yes, this い is the same as い as in だい or がい. From 明鏡国語辞典 第二版:
い
終助
① 《質問の文の後に付いて》くだけた調子で、親しみの意をこめる。 「これは何じゃい」「もう少し待ってみるかい？」
② 《肯定や命令の文の後に付いて》意味を強める。 「早くしろい」「いやだい、ぼくがやるんだい」
【語法】 助動詞「だ」「じゃ」などに付いた「だい」「じゃい」、終助詞「か」「わ」「な」に付いた「かい」「わい」「ない」、動詞の命令形に付いた「ろい」などの形で使う。
In modern Japanese, Definition ② (non-questioning sentence-end い, such as やめろい or 本当だい) is not common at all. If I understand it correctly, it's an old-fashioned, unsophisticated and shitamachi-like way of speaking, and you'll see it used mainly in manga/dramas set up in the early/middle Showa period (e.g., サザエさん, じゃりン子チエ). In fantasy works, you may hear it used by male speakers living in rural areas speaking in a curt manner, e.g., a dwarf blacksmith.
I believe it works with the imperative form of almost any verb (よく見ろい, さっさと寝ろい, 急げい, どけい, 行けい, はやくしろい, ...), but 来い is an exception. It sounds like you are urging someone.
い at the end of a question, such as 食べるかい or 調子はどうだい, is also rare in reality, but it's common among modern adult speakers in fiction. See: In what situation can I use ~かい (for interrogative question)?
