薫さん:Ah, yes. Well, in that case it depends on how you are using it. 「韻」only is translated as 'rhyme', I think. Unfortunately, the Japanese language has very few sounds, so things rhyme so much it is not unusual, and people don't notice so much. In English, of course we have rhymes in everyday speech, but for song lyrics, as you pointed out, and poetry it is intentional, and not natural. So, sometimes when we speak, and it rhymes, it sounds unusual.
Teaching children using rhymes (especially with ESL) is a valuable way to help them learn spelling in many cases, and also sounds, etc.
Anyway, 「韻を踏む」depends, as I said. For "Easy Breezy Japaneezy" (which actually used to be said a LONG time ago in the USA!) it is called 'assonance' 「母韻 ((母音だけの押韻))」, or having many of the same vowel sounds in the same line. For consonants, we have a similar thing called 'consonance' (「協和音」), like with "Whistling wildy while whipping weeds". This is also a form of what's called 'alliteration' (「頭韻」). Anyway, many native speakers also don't know these terms, because they are sort of linguistic words, but of course we all recognize examples when we hear them.
薫ちゃんさん:Thanks again for the comment, and don't worry, your English is fine. To be honest, I don't think the phrase 'easy breezy Japanesey' has too much meaning. There was an old Cockney-slang expression (Cockney is a British English dialect and very rough English) that said, "Easy-peasy", and meant something was easy to get. 'Japanesey' just rhymes, so it was added later in the US, after the second world war. Some people believe, unfortunately, that the expression was born because it meant that 'Japanese girls are easy' sexually. I think that this has something to do with the lyrics of Utada Hikaru's song; she talks about how she was used sexually and then rejected.