Is it permissible for the husband to prevent his wife from listening to lectures and the Quran and from speaking with her family over the phone while she is doing housework, and must she obey him in that?

If your listening to lectures or contacting family while at work does not affect your job, then your husband has no right to prevent you from doing so, and you are not obligated to obey him. There should be mutual understanding between spouses, and if the husband insists on his opinion, then do what he prevents you from doing in his absence.