If you know where he lived you might want to check the public library in that area (visit,call,email) and see how many high schools they had in that area and if they have yearbooks on file for those schools so you can check to see if his class photo is in the book and maybe a sports photo or a club photo.
If you know his age you can figure out about what years he was in high school.
You could also visit, call, email the public library to see if they have newspapers for the year he died and that way you could read his obit and see the names of your half siblings, their married names and children.
If you find the obit then you could go to the funeral home website and see if the death is listed there with his photo, his obit information and some sites even have friends and family post comments about the person. It might also list if he was retired or what company he worked for and sometimes what church he attended. (You could actually check to see how many funeral homes are in that area and the names and go to their websites and check their archives to see if there is a death record for your father. Usually the same obit that is in the paper is listed at the funeral home website.)
If a church is listed in his obit you might call for an appointment with the pastor/priest and just tell him that all the information you would like to know is what kind of man your birth father was since you never got to meet him. I would make sure I took all the information you have with you so he would be more likely to help you.
Who knows the Pastor/Priest may want to be a go between for you to at least meet your half siblings. You never know, they may just want to know about you.
My ex-husband and his family were surprised after their father died at age 83 that they had a half sibling that was born before their father married their mother and they never knew about him. They had DNA test done and the test proved he was their fathers child and he even had their fathers name and was a Jr.
I felt sorry for him as his mother had been dead for 20 years and he had never known his father so it was beginning to take a toll on him. He had been checking the Social Security Death Index on a regular basis to see if his father had died. Within a few weeks of his fathers death he found the death record and then his fathers obit and contacted the family.
My ex-husband and his half sibling have become good friends and he calls him brother. Good things can come of a reunion if both sides agree.
Just remember you and these half siblings are not responsible for what your/their father did or didn't do in the past.
I hope this will help you to find the information you seek and I really hope there will be a reunion between you and your half siblings. Life is short and a reunion just may give you a peace and joy in your life.