I feel your pain. My nails are constantly getting dirty too. I do not wear make up so it's just general dirt. I make sure to run my fingernails under each other when I wash my hands. I type all day too and it seems like if I keep my keyboard clean then it's not so bad. My nails are not real long either because I can't stand getting them caught in between the keys.
You could try the polishes that taste bad but my experience is that it can be picked off and may not last as long as you'd like. As for strengthening your nails, I have found that Vitamin C is great and has wonderful benefits for my nails. Of course I take a vitamin d3-5 too.
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