mix
If i understand correctly, you just need an interface that has 4 inputs right? Something like a Presonus Firebox, but im not sure how many inputs that one has.
Also, if you need a decent audio program, use REAPER man. Its free, you can make it look however you want, and you can fully customize every single detail of how it works. Once you get your 4 input box, you could even create a project template in REAPER that automatically opens up with all the inputs ready to recieve from the specific outputs on your tape machine. That way you dont have to do it every time you want to take a song off tape. Heres the link:
www.reaper.fm
Yeah i just checked, the Presonus Firebox has 4 line ins, so you could bring your tracks over all at once and be able to control the gain coming into the program. Also, there are 2 monitor outs as well as 4 line outs on the Firebox. What that means is you could use REAPERs "Re-insert" plugin to add external effects to your digital tracks, just like a normal analog mixer does. Youd just send your digital track out to your effect box, then back in one of the inputs and sent to the track with the re-insert plugin on it. Its kind of a nice feature those multiple outputs.
Or if you dont want to spend any money, just record a sound like a clap or a click at the start of the tape across all 4 tracks, then bring them into the laptop one at a time, and then line up the clap or click visually (since it will be on all the tape tracks in the same place).