I've running 2.0.10 and have had to migrate the site a few times, but each time has been smooth. What I'm noticing, though, is that there are a lot of uninstalled modules that are uploaded but not showing up on the admin modules page. Do I need to do something to update/refresh this?

One of the modules not showing up is MyDownloads. I deleted the one online and re-uploaded it, but still nothing shows up on the admin page.

Thanks for any help!

If it is not showing up to be instlled then it is not being recognised so you either have not uploaded it correctly (as in all iles arrived safe and well) or you uploaded to the wrong place, or you didn't upload from the root folder. Check out the tutorial here just to see if you did follow everything correctly.
HTH

also try turning on PHP Debug and see if there are any errors on the modules admin page

Is your system module showing up? Try updating it. Maybe because of the migration it needs to have the system updated.

This is what phpdebug gives me on a clean install ofxoops 2.0.14 when no modules are shown in modules admin to add

Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variables should be assigned by reference in file class/database/mysqldatabase.php line 239
Notice [PHP]: Only variables should be assigned by reference in file class/database/mysqldatabase.php line 239
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variables should be assigned by reference in file class/database/mysqldatabase.php line 239
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variables should be assigned by reference in file class/database/mysqldatabase.php line 239
Notice [PHP]: Only variables should be assigned by reference in file include/cp_functions.php line 57
Notice [PHP]: Only variable references should be returned by reference in file include/functions.php line 491
Notice [PHP]: Only variables should be assigned by reference in file class/database/mysqldatabase.php line 239
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259
Notice [PHP]: Only variable references should be returned by reference in file class/module.textsanitizer.php line 259

sikey: the XOOPS 2.0.14 RC1 package only comes with the system module