Is it obligatory to offer two expiations, or one expiation, or no expiation at all for someone who swore twice not to smoke and then broke his oath? And is it permissible to delay the expiation?

Smoking is forbidden (haram), and one must quit it, repent from it, and obey their mother. If you swore not to smoke and then broke your oath, you owe one expiation (kaffarah), even if you repeated the oath. The fact that you swore to your mother does not affect the obligation of the expiation. If by "necessity" you mean coercion into swearing, then one who is coerced into swearing, their oath is not valid, and they are not liable for expiation if they break it. However, if the intention was merely need or slight harm, that does not waive the expiation upon breaking the oath.