Is japa (sincere and unselfish prayer) superior to all other spiritual activities? Does it hold good for all Yugas or just in Kali Yuga ? Is there any Vedic injunction regarding the superiority of Japa Yoga over other spiritual activities/austerities ?
Yes, it is. Sri Krishna says (Gita X. 25):
...and of words I am the monosyllable "Om." Of sacrifices I am the sacrifice of japa;...
And Swami Vivekananda says (Complete Works V7, p 62):
Repeating the Om continually is the only true worship. It is not a word, it is God Himself.
And Sarada Devi, Ramakrishna Paramahamsa's holy consort, says (Adventures in Religious Life by Swami Yatiswarananda):
Devotee: "Mother, how does one realize God? Worship, Japa, Meditation--do these help one?"
Mother: "None of these can help (meaning help directly)."
Devotee: "Then how does one attain to the wisdom of God?"
Mother: "It is only through His grace. But one must practice meditation and Japa. That removes the impurities of the mind. One must practice spiritual disciplines such as worship and so forth. As one gets the fragrance of a flower by handling it, as one get the smell of sandalwood by rubbing it against a stone, on the same way one gets spiritual awakening by constantly thinking of God. But you can realise Him now if you become free from desires."
First of all Japa is not just unselfish, sincere prayer.Technically Japa is repetition of the Mantra or syllables again and again with full concentration and having in mind the meaning of the Mantra as well.
And the superiority of Japa Yajna or Japa Yoga is mentioned in KulArnava Tantram,which is one of the most important Shakta Agama Shastras.
Japa Yajnath Paro Yajno NAparohastiha Kaschana ||
Tasmajjapen DharmArthaKAmaMokshanscha SAdhayeth ||
KulArnava Tantram,Chapter 15,Verse 3.
In this world there is no Yajna which is superior to Japa Yajna,hence one should attain Dharma,Artha,Kama & Moksha through Japa.
Now,since Agamas have particular relevance and importance in Kali Yuga we can surely say that this statement is true as far as Kali is concerned.
But,we can't say, with the same amount of authority, if Japa is the best mode in all the other 3 Yugas as well.
Manu Smriti clearly says that Japaa-Yajna etc. repetition of Japa. See these mantras from Chapter 2-
An offering, consisting of muttered prayers, is ten times more efficacious than a sacrifice performed according to the rules (of the Veda); a (prayer) which is inaudible (to others) surpasses it a hundred times, and the mental (recitation of sacred texts) a thousand times.
The four Pakayagnas and those sacrifices which are enjoined by the rules (of the Veda) are all together not equal in value to a sixteenth part of the sacrifice consisting of muttered prayers.
But, undoubtedly, a Brahmana reaches the highest goal by muttering prayers only; (whether) he perform other (rites) or neglect them, he who befriends (all creatures) is declared (to be) a (true) Brahmana.