Well, you can try the following, but there is no guaranty that you will get them back. As to the moving them to the computer, you don't need to put them on a card first. You just need to connect the phone to the computer via USB cord and you can copy them or move them direct to the computer. No extra steps.
Note: If you have the backup and sync option turned on, then the following may be of help. https/support.google.com/photos/answer/6128867?co=GENIE.Platform%3DAndroid&hl=en
While there is no guaranty that you can get them back. Deleted does mean deleted. There are a few apps/programs out there that 'may' be able to help you recover the data.
A few of the programs you could try would be... DiskDigger, MobiSaver, Android-Recovery and Tenorshare. They are all data recovery apps/programs. There are many others out there, so check around and see which you would rather try. There is also one called RECUVA, that I have heard is free, which you could try.
One important note though, most of these programs are not free. They may say they are "free" or have "Free Trials" and "Free Downloads". Yet to actually recover your data, and get your files back, you may be have to purchase the program/app. Just so you know.
NOTE: For future reference, I really would suggest backing up your data to a computer or cloud. Often. Better to spend the time doing that, rather than to be out all that stuff if the phone dies, things get deleted/erased or it gets stolen.