The only type of O2 that can be brought onto the plane ( either carry on or checked) is an approved concentrator. Different airlines have different requirments, but most have the details and a form for the doctor to fill out on there web site. We always let our med supply set up our O2 when away from home. That way you can make sure that the proper things are sent and our company will even send our insurance info along so that everything gets taken care of.
As for any otehr medical supplies, they do not count toward your carry on allowance and should never be checked. Also, liquid meds can be over 3 oz.
You should have your dad check with his doctor, if he has not already done so, and make sure he is ok to fly and also his doctor may have more info on the best way for him to fly. The doctor will also have to fill out a form for the air line ( in most cases).