https://i.ebayimg.com/images/g/0zwAAOSwdxVcNY-3/s-l1600.jpg

Obviously, Out of This World during its first season, at the very least, aired on NBC's owned and operated stations (https://en.wikipedia.org/wiki/NBC_Owned_Television_Stations#Stations) as part of its "Prime Time Begins at 7:30" (https://en.wikipedia.org/wiki/Prime_Time_Begins_at_7:30) experiment:
City Station (https://en.wikipedia.org/wiki/Out_of_This_World_(TV_series)#Stations)

Atlanta WAGA 5[8] (https://www.radiodiscussions.com/showthread.php?667301-Who-aired-what-where-Lesser-known-syndicated-shows/page11)
Boston WCVB 5[9] (https://www.radiodiscussions.com/showthread.php?515501-RETRO-New-Hampshire-Today-in-1987-(Oct-3))
WFXT 25[10] (https://www.radiodiscussions.com/showthread.php?714554-Retro-Boston-MA-Wednesday-October-30-1991)
WLVI 56[11] (https://www.radiodiscussions.com/showthread.php?714540-Retro-Boston-MA-Saturday-December-16-1989)
Charlotte WBTV 3[12] (https://www.radiodiscussions.com/showthread.php?706351-Retro-Spartanburg-SC-Saturday-July-16-1988)
Charleston, South Carolina WTAT 24
Charleston, West Virginia WVAH[13] (https://www.youtube.com/watch?v=VC9oGYGPgKg)
Chicago WMAQ 5[14] (https://www.radiodiscussions.com/showthread.php?710373-Retro-Arlington-Heights-IL-Thursday-November-5-1987)
WPWR 50[15] (https://www.radiodiscussions.com/showthread.php?568842-Retro-Chicago-9-15-90)
Cleveland WUAB 43
Davenport KWQC 6[16] (https://www.radiodiscussions.com/showthread.php?578598-Retro-Western-Illinois-Sun-Mar-13-1988)
Detroit WXON 20
Durham WPTF 28[17] (https://www.radiodiscussions.com/showthread.php?477769-Retro-Raleigh-Durham-Friday-August-2-1991)
Fairbanks KTVF 11[18] (https://www.radiodiscussions.com/showthread.php?506156-Shows-from-the-1980s-amp-1990s-that-are-lost-forever)
Fort Worth KTVT 11
Grand Rapids WXMI 17[19] (https://www.youtube.com/watch?v=9r4UUH_ZBoo)
Greenville WFIX 8[20] (https://www.radiodiscussions.com/showthread.php?590862-Retro-Eastern-North-Carolina-Sat-Oct-6-1990&styleid=2)
Hartford WTIC 61[21] (https://www.radiodiscussions.com/showthread.php?467046-Retro-Hartford-New-Haven-TV-Fall-1993-independents)
Houston KHTV 39
Indianapolis WXIN 59[22] (https://www.radiodiscussions.com/showthread.php?709968-Retro-Indianapolis-Terre-Haute-Lafayette-IN-Saturday-January-20-1990)
Jacksonville WJXT 4[23] (https://www.radiodiscussions.com/showthread.php?699266-Retro-Central-Florida-Saturday-January-5-1991)
Los Angeles KNBC 4[24] (https://www.latimes.com/archives/la-xpm-1987-09-14-ca-4986-story.html)
KTLA 5[25] (https://www.youtube.com/watch?v=CJWcM5JaydE)
Miami WDZL 39[26] (https://www.radiodiscussions.com/showthread.php?704124-Retro-Miami-West-Palm-Beach-Saturday-January-21-1989)
Milwaukee WVTV 18[27] (https://www.radiodiscussions.com/showthread.php?578157-Retro-Northern-Wisconsin-Western-U-P-Michigan-Sun-Mar-10-1991)
Minneapolis KITN 9
New York WNBC 4
Oakland KTVU 2[28] (https://www.radiodiscussions.com/showthread.php?705074-Retro-Sacramento-San-Francisco-Monday-November-18-1991)
Omaha KPTM 42[29] (https://www.radiodiscussions.com/showthread.php?638017-Retro-Nebraska-Sat-May-19th-1990&styleid=2)
Paris, Ontario CIII 6[30] (https://www.radiodiscussions.com/showthread.php?441453-Prime-Time-Southwestern-Ontario-10-20-1988)
Philadelphia WPHL 17[31] (https://www.radiodiscussions.com/showthread.php?627414-Philadelphia-independents-June-1990&styleid=2)
Salt Lake City KXIV 14[32] (https://www.radiodiscussions.com/showthread.php?706019-Retro-Salt-Lake-City-Sunday-November-5-1989)
San Juan WAPA 4[33] (https://radiodiscussions.com/showthread.php?600093-Retro-Puerto-Rico-Sun-Mar-4-1990&styleid=2)
Seattle KSTW 11[34] (https://www.radiodiscussions.com/showthread.php?695654-Retro-Yakima-WA-Sun-October-27th-1991)
Secaucus WWOR 9[35] (https://www.ebay.ie/itm/Maureen-Flannigan-Donna-Pescow-Out-Of-This-World-1989-Ad-five-nights-a-week-MCA/401688688713)
Sacramento KRBK 61
Spokane KAYU 28[36] (https://www.radiodiscussions.com/showthread.php?634567-Retro-Spokane-WA-Sunday-March-13-1988)
St. Louis KPLR 11[37] (https://www.radiodiscussions.com/showthread.php?455419-KPLR-11-Saint-Louis-March-23-24-1990)
Washington, D.C. WFTY 50[38] (https://www.radiodiscussions.com/showthread.php?464251-Retro-Baltimore-and-Washington-DC-Saturday-9-14-91)
WRC 4[39] (https://www.washingtonpost.com/archive/lifestyle/1987/09/14/at-nbc-slime-time-starts-at-730/129f5e05-7975-4120-9540-29a5a44df470/)
Wichita KSAS 24[40] (https://www.radiodiscussions.com/showthread.php?604142-Retro-Kansas-Sat-May-6-1989)

San Diego: Season 1: KGTV-10; Seasons 2-3: KUSI-TV 51; Season 4: KTTY-TV 69

Is it currently airing on anything?

In Pittsburgh WTAE ran OOTW back-to-back with Small Wonder on Saturdays in 1987-88. OOTW briefly turned up on WPGH in the Fall of 1989.

Somebody here (https://moviechat.org/tt0092423/Out-of-This-World/58c748dc6b51e905f672dbd2/What-Channel-was-this-on-in-the-US-originally), also said that they recall seeing Out of This World in Dallas on channel 27, which would've been KDFI (https://en.wikipedia.org/wiki/KDFI) as well as channel 11 (KTVT (https://en.wikipedia.org/wiki/KTVT)).

Here's some print ads from its first season (https://www.ebay.com/itm/202875720755) as part of NBC (https://www.nytimes.com/1987/08/11/arts/redefining-prime-time-it-s-all-in-who-you-ask.html)'s "Prime Time Begins at 7:30" (https://www.washingtonpost.com/archive/lifestyle/1987/09/14/at-nbc-slime-time-starts-at-730/129f5e05-7975-4120-9540-29a5a44df470/) experiment (https://podcasts.apple.com/us/podcast/episode-61-primetime-starts-at-7-30/id1483290411?i=1000475634019):
https://aea46b85c8cc3b4fb6d0-3ed00f68ad84196825f833ed488607ce.ssl.cf1.rackcdn.com/158918348_maureen-flannigan-donna-pescow-out-of-this-world-1986-ad.jpg

https://pbs.twimg.com/media/EEt7sO3X4AE54rJ.jpg

And another one from the Sacramento affiliate:
https://i.ebayimg.com/images/g/LU4AAOSwq9BfVD~s/s-l400.jpg