Knives with a single bevel are really only used in Japanese and similar cookery where you need to do a lot of fine slicing, as explained by
garlichead
Let's assume that you just want to do typical Western cookery, so we can ignore single bevel and stay with typical 2- bevel Western style chef's, paring, and similar knives
In which case all the sharpeners you have described will work OK, within the limits of the particular sharpener you've chosen, and it shouldn't make any difference whether you're left or right handed
So IMO the problem is not that you're left handed, but rather that you simply don't know how to use a sharpener in the first place; and my apologies if that is a bit blunt (no pun intended!) but I'm trying to explain the situation and help you
So IMO (again!) what you should do is to learn how to use a sharpener better, and here are some suggestions -
A lot of people don't like the pull through type of sharpener as they think they're too severe, but in your case you might have to accept that if you can't sharpen a knife any other way. Try a good quality bench mounted type
Also try, and learn to use, a straightforward sharpening steel, there are loads to choose from. I don't think it should make any difference whether you're left or right handed, unless the steel is specifically labelled so
Search YouTube for videos about How to Use a Sharpening Steel; How to Sharpen a Chef's Knife with a Steel, and so on; there are loads of them, you should be able to find a method that suits you
Now & again, you could have them, (and your stash of blunt knives!) professionally sharpened
Is there a butcher or a good restaurant near you? You could ask them to give you a lesson, at a quiet time, perhaps a mid week afternoon
Most of the time I sharpen my knives on a steel, occasionally on an oil stone
I've tried whetstones, ceramic, and diamond stones, but I prefer oil stones
Sometimes you can find knives that are not supposed to require sharpening, and given brand names like staysharp, eversharp, and similar. They usually have a very fine serrated edge
I don't like them, but they're something to consider if you can't manage anything else
If you're really having problems, Search t'Net & YouTube for The Lansky Sharpening System, but it's expensive compared to a simple mid priced steel
Let us know how you go on
EDIT - the other advice, of course, is not to let your knives get blunt in the first place
Use a steel constantly, more or less every time you use your knife, certainly every few times, and before & after a long cookery session
Once a knife has become blunt it is much more difficult to bring it back to a good standard than keeping it in good condition all the time
And a sharp knife is safer & easier to use.
And of course, you're using a soft chopping board such as wood or plastic, and not something hard like glass ..... aren't you?