Is it permissible to circumvent an oath by asking another person to do what one swore to abandon, and is expiation for the oath obligatory in this case?

If you have sworn an oath not to access a website or messenger that leads to sin or wastes time, then you must uphold your oath. As for authorizing your brother to open them, this depends on your intention at the time of the oath: If your intention was not to open them yourself, then there is no harm in authorizing someone else. However, if your intention was not to enter them at all, then whether you enter them yourself or through your representative, it is considered breaking the oath, and you must pay expiation for it.