Those aren't air conjugations, those are 'aig' conjugations. aig + mi = agam. The air conjugations are orm, ort, air, oirre, oirnn, oirbh, orra. They are both used in different ways to indicate possession (along with le), and it's often a case of learning which goes with which situation. Physical possessions usually use the aig ones or le (at or with) but some things like hair and heads use the air (on) presumably because your head or hair is on you.
Only some parts are 'on' you (head, hair etc.) other parts are 'at' you (eye, mouth). Though interestingly enough, when not describing the size or colour of them, body parts are some of the few things you can use the mo/do/a/a/ar/ur possessives on. I.e. Tha mo chluas goirt - my ear is sore.
Tha beul mòr aice - is a big mouth at her. Tha beul mòr aige - is a big mouth at him So it's the aice - at her, as opposed to aige - at him. If you are asking the difference in how they sound (and indeed aca - at them) it can take a little tuning your ear into. aige is a big of a hard g, aice there's a bit softer and a bit of aspiration before the c, and aca there's again aspiration before the c but it's more of an 'ah' before the c. Though some dialects it's difficult to tell without context. If you want to be able to hear them all you might find learngaelic.scot useful.