Best software program for recovering files from formatted Mac Journaled file format drives. Or should I take to pro?

Since you haven't written anything new to those drives, there's still a chance of recovering some of the files, especially if they're traditional hard drives rather than SSDs.

I'd avoid running Disk Utility's First Aid, reformatting, or trying to repair the drives for now. Don't save anything to them, either.

The important distinction is whether the drives were simply erased or actually damaged by the electrical problem. If they're making unusual noises, disconnecting unexpectedly, or having trouble spinning up, I'd go with professional recovery rather than risk making things worse.

For a healthy drive, I'd consider R-Studio for Mac. It supports Mac OS Extended (Journaled/HFS+) and has a demo mode that lets you scan and preview recoverable files before paying.

Ideally, create a sector-by-sector image of each healthy drive onto a separate drive first, then run recovery software against that image. Save recovered files somewhere else, never onto the original drive.

One question: Are all three drives traditional spinning hard drives, and do they appear normally in Disk Utility with the correct capacities?

That would help determine whether trying software first is reasonable or whether the $300-per-drive professional option is worth considering.

If these are spinning HDDs then there is a chance of recovery (maybe incomplete, maybe data loss). If they are SSDs, then the chances of data recovery are very small.

DiskDrill is a highly-recommended utility for data recovery:

https://www.cleverfiles.com/lp/data-recovery-software.html

Taking a step back, the usual advice would be to just restore from your Time Machine backup. If you don't have one, then you have learned a lesson the hard way. There are two types of drives – those that have failed and those that have not failed yet. Besides such catastrophic occurrences, there are other situations where a backup is very helpful – if you overwrite or delete a file, for example. Apple provides an excellent utility that’s already installed on your Mac, Time Machine. 

Back up your Mac with Time Machine - Apple Support

Time Machine allows recovery of individual files and folders from prior backups. If you use the default setting of hourly backups, then you will have the option to revert hourly for the past 24 hours, then daily for the past month and weekly beyond that, to recover changed files or folders, or your whole system. That can protect you not only from a drive failure, but for example from loss/damage/theft. You can replace a Mac, and restore the old data to the new Mac from the Time Machine backup.

It’s recommended to back up to an external drive that is 2-3x the size of your internal storage. External storage is relatively inexpensive, a 1 TB SSD or a 2-4 TB HDD can be purchased for <$200 (prices have gone up significantly in recent months, unfortunately). Consider that one backup may not be enough, a commonly recommended strategy is 3-2-1 where you have three copies of your data, two of which are backups and one of which is stored offsite.

If you have not started using Time Machine to back up your Mac, now is the Time (pun intended). 

yoonmi1036 wrote:

So since these HDDs from the old Intel Mac were formatted by Disk Utility and put into storage and not touched, can they be recovered (They were Mac Journaled)?

Pick a data recovery app and see what it can do. Most of these data recovery apps will show you the files & folders it can see, but will require paying for the app in order to recover the files beyond perhaps a few small files to prove the app can recover something.

Chances are you can recover most of the data as long as it was a simple erase and not a secure erase, but...........the real important question is will that data be just generic file types or will it also include the file & folder names as well. I honestly don't know. Generally if a simple basic scan of a drive yields the files, then they will usually include file & folder names. If a deep low level scan must be used, then you will end up with millions of unknown no name files identified only by their file type (TXT, JPG, DOC, etc.).

.... were formatted by Disk Utility and put into storage and not touched,

It seems to me that the most cost-effective first step is with a bare-drive adapter that lets you mount a removed drive on a working computer's desktop like any other external drive.

I have one of these: SABRENT USB 3.0 to SATA Hard Drive Docking Station, 2.5/3.5in (EC-DFLT)

that has built-in power for 3.5-inch SATA drives, and also worked with 2.5-inch drives.

With that you can at least see if the drive shows a normal directory. If it does, your chances for rrevocering files are not too bad. If it doesn't that says it makes little sense to spend more money on expensive recovery techniques.

I should be clear that these old HDDs are from an Intel Mac—the old finer cheese grater one. (There's 4 of them) I didn't replace the Mac because the specs on the newer ones after were terrible.

And the HDD from the iMac 2019 was completely fried and replaced with a new one.

So since these HDDs from the old Intel Mac were formatted by Disk Utility and put into storage and not touched, can they be recovered (They were Mac Journaled)?