If you just want to bring the items mentioned, you can send it thru the cargo division of American Airlines.
You can break the bikes down and have them boxed in a long narrow box. Mailboxes, Etc. can pack it for you.
As long as each box is not over 70 lbs....it isn't real expensive.
Contact the cargo division at American and see what they say.
As for the microwave.....box it and bring it with you on the plane.