1)А завтра снова мир залить вставало солнце а́ло.
=>But [every time] tomorrow the sun [being] reddish got up to spill [the beans] over the world again.

2)Но странная из солнца ясь струилась...
=> But the sun was leaking a strange "brightness" ...

What's "ясь"?
It seems that Mayakovskiy made up that word based on the adjective "ясный" (=bright) based on the phrase "ясное солнце" (=the sun's bright).

3)Про то, про это говорю, что-де заела Роста
=> I'm speaking about this and that; that I'm fed up with my current job (literary "the job's been eating me").

"Что-де заела Роста" is beyond me.
=> At the time this poem was written Mayakovskiy was working among other artists for the Russian Telegraph Agency (РОСТА = РОСсийское Телеграфное Агенство) aiding for the Soviet propaganda among the masses. The artists created catchy posters and short slogans to convey pro-Soviet messages. The full name of his job was Окна сатиры РОСТа (=The satiric windows of Russian Telegraph Agency). So, Mayakovskiy complained to the Sun that he's got fed up with his job.

4)«Пойдем, поэт, взорим, вспоем у мира в сером хламе.
=> Let's go, poet, let's dawn, let's sing at the world's gray garbage

Я буду солнце лить свое, а ты — свое, стихами».
=> I will spill my sun (=the beans) and you'll spill yours by [means of your] poems

5)светить — и никаких гвоздей! Вот лозунг мой — и солнца!
=> To spill - no nails! That's the sun's slogan and mine [too].

What does "никаких гвоздей" mean?
=> "No nails" is an [obsolete] idiom meaning "that's it". Some of the idioms with the same meaning are: сливай воду, туши свет, суши сухари, точка, шабаш, суши портянки, и дело с концом, кончен бал, баста, и делу конец.