1) "I should go because it is late" is correct.
You are saying that it is late now, so present tense is what you want to use here.
2) "It was a very long day" is also correct.
This means the day passed slowly. The day is now over, so using past tense to talk about it make sense.
3) If you change this sentence to "It has been a very long day," that works too.
This means that up until the present, the day has passed slowly. Present perfect can be used to indicate an event that began in the past but is still going on. It has been a long day today, and the day is not over yet.