Ok, there are a lot of meanings in Enel's "I'm god" exclamation, both in-story and meta-commentary.
And since you said you don't read the manga and don't know the characters reactions to Enel's claims, I'm kinda assuming you meant you don't follow the series, so I'll try to give as much context as possible.
First I'll adress "Is he God or is he a god?" question.
One Piece doesn't take place in our world, so even if they were monotheistic they wouldn't have the God of Abraham (creator of the universe in the jewish, christian, and muslim texts) as we do. And while the western world mostly adopted a religion that prays to only one god, leaving many different pantheons behind (like the greek and nordic gods), in Eastern countries the biggest religions are still polytheistic and pray to many gods or divine figures.
There are still hierarchies and more important gods than others but it's very rare that when they mention god they're only mentioning One-Above-All. And that is usually reflected in how much leeway and safe space they have to create stories that mention actual gods or even create new ones.
So now lets jump into the actual story.
Enel is introduced as the ruler of an island that floats in the sky, called Skypea. He has eaten the goro-goro (or rumble-rumble) fruit which gives him power to create and control lightning, and even transform himself into electricity. He also has a very strong spiritual power called Mantra that usually allows someone to predict an opponent's next move and see their actual intentions or feelings. When he uses them together he can know/hear what the people on the entire Skypea Island are saying and if anyone says something bad about him they get almost instantly struck by lightning and are punished.
When Enel first appears he claims "Ware ga Kami nari", and this setence can be read in two ways (please note that I'm no japanese expert, I just remember what the translators explained back then and what the wiki says). "Ware ga" means "I am" and "Kaminari" means "Lightning", so "I am Lightning". But Kaminari has the root Kami, which means "god", the verb Naru, which means "To cry out/shout" as the ancient belief was that lighting and thunder were gods voices coming from the skies. So it's a pun, he's meant to say he is god and he is lighting.
He means that as he is above anyone else. He doesn't believe he created the world but he believes he's meant to rule it since he's the strongest.
Then we have the tittle used by the rulers of the sky islands, which is God/Kami. And while there may still exist reasons for them to use that tittle that we the audience don't know yet, to them it's just a tittle. It doesn't mean they see themselves as creators of the world or that they're divine, it was simply the name the rulers of Skypea used instead of saying king or president, until Enel came along and actually started playing the part of an autoritarian and vengeful god.
Now onto how the characters and the StrawHats reacted to Enel's claims of godhood.
Many characters, specially the inhabitants of Skypea, do start to fear Enel as a god and believe his claims since the Mantra ability is very very rare and devil fruit powers are even rarer. To them he does seem omnipresent and omnipotent, but our protagonists, being more experienced in travelling the world, can see Enel for what he actually is: a man with very powerful abilities but not actually a god.
Some express a possible existence of god but Enel is not Him, some outright claim not to believe in god, and Luffy just doesn't care if he's god or not. Enel is being mean to his friends so Luffy will beat him no matter who or what he is. And since Luffy's power is that he's made of rubber he is Enel's natural enemy, as he cannot be electrocuted.
And this last point brings us to a theme that One Piece also explored outside of the Skypea arc.
Luffy's full name is Monkey D. Luffy and many characters have mentioned in the story that people from the D. clan are the natural enemies of the gods.
Besides Enel other characters use the titles of God. The Celestial Dragons are the members of the original royal families that established the current World Government that live atop of rest of the world and since their ancestors did shape the world into their liking they call themselves gods and the rest of the planet are just lowly people.
Luffy was not only Enel's natural enemy, due to their powers, but is also the enemy of the opressing class, the Celestial Dragons, since he aims to be as free as possible in his adventures.
The gods presented in One Piece are very rarely portrayed as kind or just divine beings, they are usually mortal men who for some reason or another sit above the common folk and try to control their lifes with authority and opression. They are meant to be the biggest obstacles faced by the protagonists of the story who fight to protect the weak and those who are actually kind and giving.
I hope this long ass post makes sense to you and that it answers what you were looking for.
If you have more questions about it or need more clarity or context in any of the points, feel free to ask.
