For his change to be truly successful, your father will have to want to discard some of the items that he has hoarded. If he does not want to do this, it will be difficult for him to change.
There are several ways to approach this situation. First, you could have a family meeting, where you and everyone else in your family sit down with your father and tell him how all of the stuff in the house is having a negative impact on you and how you are embarrassed to have people come over. Do not do this in an accusatory manner, but just be frank and let him know how you feel about the situation.
If he is willing to get some help, let him know that you will help in any way you can and that you know this will be difficult for him. If he is not willing to get help, then there are other options, however, just throwing out all of the stuff when he is not around is probably not a good idea. That would most likely make him very angry and would also probably make the hoarding worse because there is a good chance that he would seek out more items to fill the void that you created by purging everything he already had.
One option that you have is to tell him that if he is not going to get help, the rest of the family will be moving into an apartment. Many families have done this in the past, some for sanitary and health reasons and others because they just could not stand living in such conditions anymore.
You and the rest of your family can decide what rules to have at the apartment, what comes in and what gets thrown out. If your father chooses to visit, you can set it up so that he is not allowed to bring anything into the apartment other than one change of clothing and toiletries. Otherwise, he must keep the hoarding to the home. Although this may not be convenient, it is what some families have had to do.
Unfortunately, you cannot make your father change his behavior. You can, however, let him know how his behavior has impacted you and show him that you are willing to either help him or do something to place yourself in an environment where you will feel safe and comfortable.