Based on your description I would guess that you have classical guitars. The three lower strings are metal windings around a silk or nylon core. I would not put steel strings on them. I would recommend taking them to a luthier for an assessment of the damage and what it would take to bring them back to good playable condition. In addition to damage you can see on the outside, there may be loose or damaged braces on the inside or other issues that an untrained eye just wouldn't catch.
Sometimes in cases like yours it turns out that it would cost more to repair them than what the guitars are worth. Then you would need to decide if the sentimental value you attach to them makes it worth it to you to spend the money to have them repaired.
Converting a right-handed guitar to left-handed isn't as simple as putting the strings on upside-down. On a classical it is easier because usually the saddle is not angled, so all you need is a new nut, and sometimes the existing nut can even be re-worked to work.
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