Literary estates and executors. Sometimes, a famous author names a literary executor in the author's will. The literary executor differs from a traditional executor; the literary executor just manages copyrights and manuscripts on behalf of the estate. (Here's a good explanation of how it works.) When a literary executor is named, the executor often operates on behalf of "Estate of [Author Name]." In some cases, a trust or other business entity is established to manage those works. That may make sense for tax purposes. Keep in mind that you can operate informally as a partnership, too.
Recording ownership changes. If you wish, you can simply record a statement with the Copyright Office indicating that you and your siblings have inherited the copyrights (to make it easier for others to find the owners). If a new version of your father's work is published, you (and your sibling co-owners) can be listed as copyright claimants on the copyright application. In Section 3 of Form CO, check the box indicating you inherited the copyright.
Co-ownership arrangements. As co-owners of the copyrights, any sibling can make licensing deals provided that the person making the deal accounts to the other co-owners and provided that it is not an outright sale (assignment) or exclusive license of all rights to the novel (see # 4 in this article). Many co-owners who inherit don't want the ongoing hassle and tax reporting so they sell or trade their rights to one sibling. If you form an entity, even a partnership, it's best to enter into a co-ownership arrangement in which a division of duties and revenues are established.
Where can you learn more? You can learn more about registering literary works and recording documents at the Copyright Office in Steve Fishman's Copyright Handbook. And this PDF from ASCAP (even though it deals with musical works) offers one of the better explanations of issues that arise when copyrights are inherited.
Housekeeping. What deals currently exist? Create a list with relevant info; you may be able to terminate some of these. In any case, notify the people who are still paying royalties of the change in ownership so that you can continue to receive income. It's probably a good idea to consult with a tax specialist, particularly if the books are generating thousands of dollars in revenue.