I've never heard of "adverbial nouns" in Japanese, nor the supposed 副詞的名詞 mentioned on the template page, and that's after studying Japanese for over 20 years and working as a professional translator for over 10. No dictionary I have to hand contains the term 副詞的名詞, and it's redlinked here (as it should be). Nothing links to the template and the cat is empty -- can we delete the template and the cat, please? -- Eiríkr Útlendi | Tala við mig 15:54, 16 September 2011 (UTC)
Searching the web, the only hits for "Japanese adverbial noun" are from http://www.orientaloutpost.com, in the form "Japanese (adverbial noun)". The fact that Google Scholar gets zero hits tells me these should be deleted. Mglovesfun (talk) 10:50, 25 September 2011 (UTC)
一 (ichi), 一つ (hitotsu), 一丁 (icchō), 一両 (ichiryō): These are actually numbers and counters, not adverbial nouns.
一度 (ichido, hitotabi), ひと度 (hitotabi): Nouns, meaning "one time" or "once". These time-related nouns can be used with or without a following particle (usually に, but depends on context) -- but then again, all Japanese nouns can leave off the particle in certain contexts when the grammatical role is clear, and that doesn't make them "objective nouns" or "dative nouns".
この先 (kono saki), 今後共 (kongo to mo): Mis-analysis. The first is a noun phrase, "this time", that can be treated the same as 一度 above. The second is again a phrase, "next time as well", but it includes the postpositional particle combination とも "as well", just spelled in kanji as 共 - so there's no way for this full phrase to be just a noun, adverbial or otherwise.
Given the miscategorization of these various terms and phrases, I'm not sure how trustworthy Oriental Outpost is. Somewhat in their defense, describing another language's grammar is always tricky, especially when the language being described is far-removed from the language being used for the description. That said, I'm not a fan of the "adverbial noun" category, and as Mglovesfun notes, the Google-able web seems to agree. -- Cheers, Eiríkr Útlendi | Tala við mig 18:48, 25 September 2011 (UTC)