I'm afraid it's probably bad news.
Hallmarks of a bad acoustic guitar include:
- thick, heavy neck
- poor intonation
- wood with poor acoustic qualities
- rattles and buzzes
Here I'm talking about the very cheapest guitars on the market - sold at market stalls, supermarkets and toyshops. From your statement "it sounds bad even to an amateur like me", it seems likely that's what you have.
Of these, few can be remedied -- if you could make a very cheap guitar sound great, there would be no point in more expensive guitars!
The thickness of the neck isn't really something you can fix.
Intonation issues can sometimes be fixed by adjusting the bridge - but it's likely that your bridge is fixed, so this would be difficult. If there is a problem with the positioning of the frets, it's not practical to fix.
The wood that makes up the body affects the tone of the guitar. Good guitar woods resonate and colour the sound in pleasant ways. Cheap acoustic guitars use plywood, which absorbs vibration. You can't practically replace this wood - it would be cheaper to just buy another guitar.
Rattles and buzzes can sometimes be fixed by re-glueing internal bracing and frets, bridge, nut etc. However you say you are not experiencing buzzing.
You can safely put nylon strings on a guitar designed for steel strings, because the tension of nylon is much lower. However it is unlikely to sound good. Guitars designed for steel strings, are designed to sound best with steel strings. (Tautological, I know, but the question was asked).
You should not put steel strings on a guitar designed for nylon -- the tension will damage the instrument (and maybe you).
Instruments designed for steel strings can usually be identified by the presence of a truss rod in the neck. You can tell there's a truss rod if you can find its adjustment screw - either tucked under the sound hole, or under a panel in the head.
The best way to make a bad instrument sound good, is to play it really well! If you can't afford a better instrument, by all means use this this one until you can afford better.
However, if you're learning, do bear in mind that a bad instrument can hold you back badly. I spent years struggling with barre chords simply because I had a badly made guitar with ridiculously high action.