Some russian ships were fitted with the "Дракон-128C" (Dragon) active sonar (either a 1:1 copy or a straight british ASDIC). From what I've dug up, at least one destroyer of the Black Sea Fleet has been fitted with it:
http://flot.sevastopol.info/ship/esminets/sposobniy.htm (link in Russian)
This page (link in russian too):
http://forums.airbase.ru/2002/01/t8788--esmincy.html
mentions some of the "Project 7"-destroyers (the backbone of the russian destroyer Fleet in WWII) having been fitted with the Dragon at one point or another. More detailed info might be found here (following links in russian):
http://www.wunderwaffe.narod.ru/Maga...6_02/index.htm
(monography on the "Project 7" destroyers)
maybe more here:
http://www.wunderwaffe.narod.ru/Maga...7_06/index.htm
(same, but for the improved 7У version)
and here:
http://www.wunderwaffe.narod.ru/Maga...8_06/index.htm
(monography on the Leningrad-Class destroyer leaders)
More books from the same website mention also certain russian submarines of the Pike and S-Class being outfitted with ASDIC late in the war (predominantly in the Northern Fleet)
Sorry, I am too busy/lazy to dig out and translate the detailed info. Also, these sources leave one uncertainity - was the Dragon just an ASDIC Copy or a russian development based on it and if it was a copy, was there also a genuine russian-developed ASDIC as well.
As for the popular sub hunters of the MO (Малый охотник - literally "small hunter") class (deployed in large quantities in the Black Sea, I didn't find any info on them being fitted with ASDIC.
Hope that helps a bit.