How would I go about finding the family trees of all the gods and goddesses in all mythologies?
I don't have an easy answer for you, but I do have an idea to get you started. I teach AP literature and composition, and as part of their summer reading I want my students to review their mythologies. The book I ask them to read is Edith Hamilton's Mythology. (I know--pretty obvious title, isn't it.)
This text is an extensive, thorough review of Greek and Roman gods, which of course are the most commonly studied. It does give cursory coverage of the Norse gods, as well. She does offer a genealogy of sorts, but it isn't as comprehensive as your question implies you would like (all the gods in all the mythologies).
A quick search on line tells me you could probably find a family tree for each mythological family if you spent the time to look, and I've included an enotes link to Hamilton's book so you can check it out for yourself. Hope that gets you started, at least!
On its home page, the web site greekmythology.com has a family tree of the principal Greek gods (meaning the siblings and children of Zeus) and a few of their children. Just click on the link in the Sources section, and you go right there.
Wikipedia has a more extensive family tree. It begins with Chaos and includes all the demigods (children of Greek gods with humans). All of the names are hyperlinked, so that you can click on any member of that family tree to get his or her story. I've pasted that link in the sources section also.
I hope this helps you!
I did a project like this a long time ago. It was pre-computer, so here's how I'd do it today.
First, obtain some software like Family Tree (there are free versions out there).
Next, pick any god/goddess at random. Find out who their children were; if they are Greek deities, you'll find a lot, many illegitimate, but that's part of the fun.
Follow the family lines, and have fun!