Why did the Ghostbusters go with Louis Tully as their lawyer?

They're broke

As far as I can tell, the Ghostbusters' primary motivation for hiring Tully is financial. They've been barred from engaging in any "ghostbusting" activities and have apparently faced multiple lawsuits from the City over the intervening few months. Having been forced into entertaining at children's parties to make ends meet, Louis Tully is the quite literally the best legal mind that they can afford.

Hardemeyer emitted a harsh laugh. "I know who you are, Dr. Venkman. Busted any ghosts lately?"
"No," Venkman admitted. "That's what I want to talk to the mayor about. We did a little job for the city a while back and we ended up getting sued, screwed, and tattooed by desk worms like you."
Hardemeyer offered Venkman an angry stare. "Look," he replied, bristling. "You stay away from the mayor. Next fall, barring a disaster, he's going to be elected governor of this state, and the last thing we need is for him to be associated with two-bit frauds and publicity hounds like you and your friends. You read me?" - _{^{Ghostbusters II - The Novel}}

In addition they (or at least Egon and Venkman) feel that their case is essentially unwinnable. Not only are their charges being tried by the meanest judge in town (someone that Egon identifies as "The Hammer") but they're also facing the city's own legal squad and the might of the Mayor's office. They unquestionably did the crime and, barring a miracle, they're going to do the time. Paying for a high-priced lawyer would be an indulgence even if they had the money to do so.

Peter Venkman found himself on the stand, facing his own lawyer, the rattled, diminutive Louis. Louis had been babbling for about a minute, Venkman encouraging him with a helpful nod, a wink, or a hearty "Hear, hear." That gave Venkman the chance to think of what he would do when he was finally paroled. Not much, he concluded. - Ghostbusters II, the Novel

He won the case, didn't he!

Seriously though, there is an arguable reason for hiring him. In the script, before Moranis comments on their mistake:

JUDGE: I want to make one thing very clear before we go any further. The law does not recognize the existence of ghosts, and I don't believe in them either, so I don't want to hear a lot of malarkey about goblins and spooks and demons. We're going to stick to the facts in this case and save the ghost stories for the kiddies. Understood?

DEFENSE TABLE. Stantz leans over and whispers to Spengler.

STANTZ: Seems like a pretty open-minded guy, huh?

SPENGLER: His nickname is "The Hammer."

Stantz and Spengler are seated with their attorney LOUIS TULLY, lawyer, CPA and former demonic possession victim. Louis is desperately paging through a mountain of legal textbooks.

LOUIS: (nervous) I think you're making a big mistake here, fellas. I do mostly tax law and some probate stuff occasionally. I got my law degree at night school.

STANTZ: That's all right. We got arrested at night.

I'd suggest that given the judge's complete disregard for the Ghostbusters and their ghostly world, it was important to the team to have an attorney who actually believed in them, rather than some intelligent attorney who regarded them as quacks.

As you rightly say, the ghostbusters are highly intelligent individuals. But they're also highly unusual individuals, given their work. Perhaps it meant more to them to have someone value that, than "win" their case by discrediting them.

On another note, a very possible answer is also "Because." Given the severity of the charges they faced, it's of course logical they would take on serious legal help, instead of a night lawyer. But sticking with Louis, we have more Rick Moranis screen time and funny side story to the main plot. So whilst this reason is "out of universe", it's also very plausible.