A126: Countersong and Distraction are both explicit about what they can counter:

Countersong (Su): At 1st level, a bard learns to counter magic effects that depend on sound (but not spells that have verbal components.) Each round of the countersong he makes a Perform (keyboard, percussion, wind, string, or sing) skill check. Any creature within 30 feet of the bard (including the bard himself) that is affected by a sonic or language-dependent magical attack may use the bard’s Perform check result in place of its saving throw if, after the saving throw is rolled, the Perform check result proves to be higher. If a creature within range of the countersong is already under the effect of a non-instantaneous sonic or language-dependent magical attack, it gains another saving throw against the effect each round it hears the countersong, but it must use the bard’s Perform skill check result for the save. Countersong does not work on effects that don’t allow saves. Countersong relies on audible components.

Distraction (Su): At 1st level, a bard can use his performance to counter magic effects that depend on sight. Each round of the Distraction, he makes a Perform (act, comedy, dance, or oratory) skill check. Any creature within 30 feet of the bard (including the bard himself) that is affected by an illusion (pattern) or illusion (figment) magical attack may use the bard’s Perform check result in place of its saving throw if, after the saving throw is rolled, the Perform check result proves to be higher. If a creature within range of the Distraction is already under the effect of a non-instantaneous illusion (pattern) or illusion (figment) magical attack, it gains another saving throw against the effect each round it sees the Distraction, but it must use the bard’s Perform check result for the save. Distraction does not work on effects that don’t allow saves. Distraction relies on visual components.
A gaze attack is not a figment or pattern, so Distraction provides no protection from it. A banshee's wail works like Wail of the Banshee, which is a sonic effect, so Countersong should work against it (though the sicken effect works even if you save, so Countersong does nothing there.)