Q. Can you listen to a Toiro tape on the Nitl night?
A. This Shayleh actually is mentioned responsa Chai Binyomin (p. 301) where he argues that although you comply with the mitzvah of learning Torah just by listening and thinking (O.H. 47, 4 and Biur Halocho ibid.), since you do not make a brocho, (see Mishnah Berura ibid.) this form of learning may be different enough to permit it on Nit"l night.
Nitey Gavriel (Hanukah end of Volume p. 247) also permits thinking Torah thoughts on Leil Nit"l, basing this conclusion on the opinion that angels do not know the thoughts of humans.
Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit"a