The best option is probably the Beis Din of your own community; see if they are reachable by phone; they may well be. That said, someone I sort of know has experience with the following hotlines in the States.
(I am not in a position to judge their halachic permissibility or reliability. It seems that you should tell the rabbi on the hotline whose minhag and opinions you usually follow, though perhaps they will ask, if it is necessary to know.)
845-HALACHA -- Monsey, I think. It's either 24/7 or 24/6, and I believe it lets you choose language, as well as whether you want a litvish or chassidish or sefardic or maybe other type of dayan.
516-239-2500 / 718-337-8370 -- The Halacha Hotline of the Five Towns and Far Rockaway Community under the leadership of Rabbi Binyomin Forst. One of the numbers may be a pay-per-minute number, but they will quickly tell you how to call them for free if you express a need. Seemingly not available Shabbos or Yom Tov.
718-604-8000 -- The Beis Din of Crown Heights. Chabad. At least one dayan is usually available during business hours. Some phone numbers for other hours are listed here. (I suggest you pay mas hakohol if you are from the community and/or you are using them a lot.)
Others I found on Google and know little about:
(732) 363-1616 / (908) 670-1596 / 732.905.9992 - Bais Horaah of Lakewood. 24 hours. Paid; for details see here.
1.844.200.TSHC (8742) / call or text 732.9300.SHC (742) / 732.276.2173 -- The Sephardic Halacha Center/Rabbi Ariel Ovadia. Details here.
877-845-8455 -- For questions about business halacha.
1- 877-963-8938 and international numbers here -- Women's health questions. Limited hours; see link.
855-482-4272 -- Tahareinu (confidential taharas hamishpacha hotline). Israel, Canada, UK, Belgium numbers here.
718-951-3696 -- Shmiras Haloshon questions. From 9:00 to 10:30 p.m. (east coast time) Monday thru Thursday and Saturday nights.
410-484-4110 x238. -- Star-K kosher hotline, under the guidance of HaRav Mordechai Frankel; you may have to leave a message.
International numbers,in addition to those above:
Israel KAV HALACHA HOTLINE 02-569-5103 Halacha Shailos Hotline for the English speaking community -24 Hours a day (From 2am until 5:30am only urgent shailos). Momenus (Choshen Mishpat/Ribbis) 2-3pm and 9-11pm at Ext. 3. Sephardi Line, Sun-Tues 8:30-11pm and Fri 1pm until Shabbat at Ext 2. For the complete schedule or to donate, email [email protected]
416-785-7902 or Rabbi Chanoch Ehrentreu at 416-712-9752-- Kollel Toronto, Canada. The first number is available M-F from 9:30 to 10:30 Toronto time; the second is for time-sensitive questions at other times. May also be reachable in the US.
0825 660 660 (France), 0747 268 268 (Israel), 022 519 0555 (Switzerland), 514 446 9111 (Canada) -- French-language hotlines, more information here