Midorima says "-nanodayou" a lot in the anime and the subs just put it as "-nanodayou" but what does it actually mean ? Does it have anything to do with Oha-Asa ?
Nanodayo (なのだよ) is about the English equivalent of " 's-n-such " So a sentence of "Orenji o hirou nanodayo" would translate to "Pick up the oranges'-n-such".
"N-stuff" is also a good equivalent. Like "I have to go to school-n-stuff."
It could also mean "and so forth" .
I find that this source gives a relatively accurate description of the way Midorima uses the phrase: "Nanodayo" (...) adds a tone of 'an explanation about something that doesn't really need explaining' to his words."
'Nanoda' is a form of the verb "to be"（in this case simply 'da' / だ）, used to indicate assertion / a 'decisive' tone, whereas yo / よ gives a nuance of 'presenting new information' to someone or of 'trying to convince' someone. In actual usage, the effect 'nanodayo' has is somewhat similar to saying "This is fact.", "That is how it is." or "It is so." after making a statement. However, since the expression incorporates a form of the verb 'to be', there is no way to actually translate it.
I am unable to comment on other answers, but I want to correct the previous one, so I'll add this here: The English "n-such" is an absolutely incorrect translation for 'nanodayo'. とか ("toka") or みたいな ("mitai na") or 的な ("teki na") or など ("nado") at the end of a word/sentence would all more-or-less correspond to "n-such" in Japanese in different contexts. However, 'nanodayo' does not correspond to this particular phrase in any context.
Here, a native Japanese speaker answers the same question: なのだよ とはどういう意味ですか? = "What does なのだよ (nanodayo) mean?". They say it's "mainly something a CEO might say to their subordinates, and other than that it's not really in common use". Sound like "n-such"?
Also, the "orenji wo hirou nanodayo" example given in the Yahoo answer and quoted in the previous answer here is bad grammar. More correctly, it would be "orenji wo hirou nodayo" / オレンジを拾うのだよ, which simply means "(I'm going to / lets / we must / you must / etc) pick up the oranges". An anime character might use "nanodayo" more freely for comedy or for a "moe" effect, but this is not the case for Midorima (at least in canon situations).
In conclusion, なのだよ ("nanodayo") is simply an assertive way to say "is", "am", "are" or "be" (the equivalent for "were", "was" and "been" would be だったのだよ / dattanodayo). There is no English equivalent.