The word used in Nehemiah 8:10 is Strong's H4477. The verse actually says, "...and drink the sweet." H4477 is the word for "sweet" used here. When researching the meaning of the word, I found that H4477 comes from H4985. According to Brown-Driver-Briggs Lexicon:
"STRONGS H4985:
Abbreviations† מָתֹק verb become or be sweet, pleasant (Late Hebrew מתק, especially Pi.; Assyrian [matâḳu] be sweet, in derivatives; Ethiopic bdb060805 sweet; Aramaic bdb060806 suck (with pleasure), מְתַק id., be sweet; Arabic bdb060807 (bdb060807a before bdb060807b) see smack the lips (with pleasure), bdb060808 sweetness); —
Qal Perfect 3rd person masculine singular suffix מְתָקוֺ [H4988 Job 24:20]; 3rd person plural plural מָֽתְקוּ Job 21:33; Imperfect 3rd person masculine plural יִמְתָּ֑קוּ Proverbs 9:17, וַיִמְתְּקוּ Exodus 15:25; —
- literally become sweet, of water (opposed to מָרִים) Exodus 15:25 (J); are (i.e. taste) sweet, מַיִם גְּנוּבִים יִמ׳ Proverbs 9:17 (figurative of delights of illicit pleasure).
- = be pleasant, מָֽתְקוּ לוֺ Job 21:33 sweet (pleasant) to him are the clods of the valley (said of one resting in the grave).
- suck (Aramaic sense, compare Syriac above) מְתָקוֺ רִמָּה [H4988 Job 24:20] the worm doth suck him, feast on him (on verb masculine compare Ges§ 145. 7 KöSynt. § 345 a DaSynt. § 113 (b)), Di De Buhl (compare Kau Da; also SS who render 'angenehm finden'), but this sense in Hebrew dubious; text perhaps corrupt (compare conjectures by Bu Du).
Hiph. Imperfect 3rd person feminine singular אִם תַּמְתִּיק בְּפִיו רָעָה Job 20:12 if evil gives a sweet taste in his mouth (declarative Hiph.); 1st person plural אֲשֶׁר יַחְדָּו נַמְתִּיק סוֺד Psalm 55:15 [Psalm 55:14] we who used to make sweet (our) intimacy."
When talking about the "strong drink" referred to in Luke 1:15 (note: You accidentally made a typo and said it was 1:16, but the verse you referred to was actually verse 15 ;) ), Strong's G4608 is used, and from the definition I found, it is different from wine. Here is the definition I found:
"strong drink, an intoxicating beverage, different from wine; it was a artificial product, made of a mixture of sweet ingredients, whether derived from grain and vegetables, or from the juice of fruits (dates), or a decoction of honey"
I think this gives us a good idea of what the drinks consisted of.