How does amiodarone act as an alpha and beta blocker?
Amiodarone inhibits sodium, potassium and calcium currents. Its major antiarrhythmic properties are thought to be related to prolongation of the
action potential duration. Amiodarone also exerts an antiadrenergic
effect by non competitively inhibiting alpha- and beta-receptors (Ghuran &amp; Camm, 2000).

Alpha blockers relax certain muscles and help small blood vessels remain open by antagonizing norepinephrine's tightening effects on the muscles in the walls of smaller arteries and veins, which improves blood flow and lowers blood pressure (Mayo Clinic). Beta blockers decrease the effects of epinephrine (adrenaline), reducing heart rate and reducing its force, thereby reducing blood pressure. Beta blockers also help blood vessels open up to improve blood flow (Mayo Clinic). 

Alpha-adrenergic receptors and Beta-adrenergic receptors are G-protein coupled receptors (Wallukat, 2002). Hence, they do not form channels and your notes are incorrect. The ion currents are mediated by channels, though. 

References
- Ghuran &amp; Camm, J Clin Basic Cardiol (2000); 3: 206
- Wallukat, Herz (2002); 27(7): 683-90