Keep in mind too that you don't necessarily have to play all the strings all the time. Usually with barre chords on an acoustic I tend to use them mostly as power chords and only fully barre the chord if it's absolutely necessary to hear the upper notes. There's alternate ways of doing barre chords too, like with A and B you can leave the top 1st and 2nd strings open or hold a chord in the shape of a barre chord with 4 fingers and just leave out the bottom note.
The basic answer though is that even if you've got years of experience, trying to hold down barre chords on a cheap acoustic guitar isn't worth the effort.
Either get a better guitar or transpose your tunes so you don't need em.