I have difficulty distinguishing the two phonetic symbols. Roads, rose; needs, knees... Do these words sound very different to native speakers? How should I pronounce them?
With /dz/ the tongue (almost) taps against the alveolar ridge (similar to /d/) before pronouncing the subsequent /z/. This does not happen with /z/, as a matter of course.
Pronounce repeatedly /d/ followed by /z/. With each repetition reduce the distance between the two. Don't try to pronounce a perfect /d/ before the /z/ as the /d/ is a reduced one and the /z/ dominates. You got it if you not even need to move the tonge in order to pronounce both subsequent sounds. Then, the tongue is prepared for the pronunciation of /z/ (by means of its very tip) and of /d/ (by means of its upper front part). The d explosion happens between the alveolar ridge and the upper front part of the tongue and is followed directly by the z pronunciation.
Yes, /dz/ and /z/ sound very different to native speakers, and when pronounced properly are clearly distinguishable.
It is actually far more common for /dz/ and /ts/ to be confused by non-native speakers, but even these are distinct.
As to how they should be pronounced - you should pronounce them as per pronunciation guides! Some sounds in any language can pose problems for non-native speakers, but if you try your best, native speakers can more easily use wider context to make up for slight deviations in pronunciation.