Short answer: If the characters are truly PD, you can use them as if you legally owned them.
Is this character public domain?
I'm not a lawyer, so don't quote me or anyone else on these boards, but as far as we know, Dynamite Thor and most of the other characters listed on PDSH wiki first appeared in comic stories which are now (as far as we know) public domain. There is a wealth of info on the net and on these boards about how to determine if a character is PD (usually they are very old, or were created by a company that went out of business before it could renew copyright), but it is always a good idea to look up the history of a character and find out why the stories they appeared in are considered public domain, just to protect yourself from getting faulty second-hand info. I think Dynamite Thor is pretty safely and securely in the public domain.
Any information that you first learn about a character in a public domain story, is not protected by copyright. So, if "Superdude" appears in "The Adventures of Superdude #1-10", and #1-5 has fallen into public domain, any information you learn about Superdude in issues #1-5 is no longer protected and can be used by anyone. But if you don't find out about Superdude's electricity breath until issue #7 and you don't find out that his middle name is Danger until issue #8, then your version of Superdude can't have electricity breath or have Danger as his middle name. If you give Superdude atomic death vision in your stories, then nobody else can give him atomic death vision without your permission.
How can I use this character?
Assuming a character is public domain, you can use them in any way you want (in professional works as well), without anyone giving you permission. It's like making a story about Santa Clause or George Washington...nobody can sue you for using those characters, because nobody owns them. Somebody might try to claim ownership, but if the characters are truly PD, nobody can claim them.
The only thing you have to look out for is trademark infringement. You have to find out if somebody is already selling a product with the name that you gave your product. For example, there is a PD character named Daredevil. But try to print a comic about him called "Daredevil" and you will be promptly sued by Marvel. That's like trying to sell a computer called an "Apple." You can't legally do that. You can however, call any character Daredevil inside a comic book...as long as there is no confusion between your product and Marvel's product when someone buys your comic. If the cover of your comic says "In this issue, Superdude battles Daredevil," then people might think that the Marvel Daredevil is featured in the comic...so Marvel can sue you for that. You're taking sales away from them using the power of the brand name they built, and simultaneously erroding the power of that brand name by making it less unique.
However, as you pointed out, Dynamite Thor and Brick Bat are stupid names. I seriously doubt anyone owns the trademark on them. Just don't be stupid and make Dynamite Thor easy to confuse with Marvel Thor.