- bekommen: means to get something. this is the most generic term in the group since it has the least implications of how and what. It implies only that the process is finished as opposed to "empfangen".
- erhalten: means to receive something that you have expected, waited for, exclusive for objects. It could be a letter and the term "halten" (= "hold") indicates that it usually is something that is small enough to hold in your hands.
- entgegennehmen: means to take something that someone hands over to you in a more official manner, like for a registered letter. It implies that the object becomes your possession or that you act for a company to officially receive something. The term "nehmen" (="take") indicates also that you can hold it in your hands, like a letter.
- empfangen: means to receive something or someone that comes to you. It does not indicate how you got it (in your hands or not), so it is used for emails, and can be used for something continuous like a Radio signal. It implies that you are passively standing but actively wait for something to arrive, like guests.
- besorgen: means to go somewhere and get something, like shopping or if you went to get it from a friend.
- kriegen: means a passive receiving of something. It can indicate that you had little or no control in getting it. It could be taken as almost 100% equivalent to "bekommen" in a colloquial form.
Please note that bekommen and kriegen can both change the meaning with the appropriate preposition: Herausbekommen, hinkriegen, rauskriegen