i'm not really sure if you are asking the therapeutic uses of these drugs, but as you already know what receptors they hit, that is where i will focus.
dopamine: for shock can increase cardiac output thereby increasing tissue perfusion, dilates the renal blood vessels improving renal perfusion and decreases the risk of renal failure.
for heart failure, it increases cardiac output by increasing myocardial contractility. indicated for the management of cardiogenic and circulatory shock.
dobutamine: in heart failure increases myocardial contractility and improves cardiac performance. since it does not activate alpha 1 receptor, it doesn't increase vascular resistance. it is generally preferred over dopamine in the short-term treatment of chf.
epinephrine: this is used to delay the absorption of local anesthetics, control superficial bleeding, decrease nasal congestion and elevate bp, overcome a-v block (unknown what degree), and restore cardiac function in patients who have arrested. it is also the treatment of choice for anaphylactic shock. this drug is much more potent than dopamine, so the effective dosing range is less than that of dopamine.
levophed (norepinephrine): although similar to epinephrine, it has limited clinical applications: hypotensive states and cardiac arrest
cardiac output is increased only at low doses. with high doses, the cardiac output decreases in response to the vasoconstriction and increased afterload ( stress or tension placed on the ventricular wall during systole).
i'm sorry that i wasn't able to find information about neo...i have seen it used in a hypovolemic shock situation where we weren't able to raise the blood pressure with volume via iv. in this particular person, the bp raised for maybe 5 minutes before it dropped off again. i think that the doctor's really expected that he would be dry (he had a perforated gallbladder that was necrotic, and they removed 2+ liters of bile from the peritineum).
my sources for this information was the icu book, second edition by paul marino (i refer to this all the time, it is very helpful if you are a new ccu rn). i also used the second edition of pharmacology for nursing care by richard lehne, linda moore, leena crosby, and diane hamilton. i hope that this helps.
p.s. the gentlemen that i took care of with the gallbladder did live, was sent to another hospital for more invasive monitoring than my hospital is able to do and walked back in to see us.