This is my attempt
Ikuzo
行くぞ
"Here I go"
Turn up radio sou kyou mo kikoeru yo
Turn up radio そう今日も聞こえるよ
"Turn up the radio, yeah that's right, I can hear it again today!"
Kaze ni yurare nagareru stereo
風に揺られ流れるステレオ
"The stereo [sound] riding on the wind"
Kata de kizamu keikai no rhythm
肩で刻む軽快のrhythm
"Shoulders cutting out the funky rhythm" [like you are marking the rhythm by moving your shoulders, I think]
Omoi wo nokkete todokeru yo rhyme
思いを乗っけて届けるよrhyme
"The rhyme transmitting [our] feelings"
Yoku hareta sora no mashita
よく晴れた空の真下
"Right under the sky that's now cleared [for us]"
Yes yet again I forgot to look up the kanji before I started, least this wasn't too bad, except I wasn't sure which "kata" it was. I'm not 100% sure about the yoku, I think it is like when someone does you a favor, like "yoku kita na", like the sky was "kind enough" to clear up.
As for translating songs, I would suggest finding a bit that you can recognise the kanji for, and sticking it into Google. It's a lot easier to translate kanji than romaji, though it might take longer if you have to look each one up.