Impedance matching in multi-layer circuits
With 4 layers, you can make microstrip, embedded microstrip, or asymmetric stripline. Use whichever one suits your needs the best. 

Outer layer microstrip will probably use the least board area for a given set of interconnections.

Asymmetric stripline will provide the best shielding, but remember you will need unbroken ground planes both above and below the track, which will restrict how you can route other lines.


  since there will be other traces to match that are close to each other, will they influence each other?


A usual rule of thumb is to make sure uncoupled tracks are placed at least 10x the track width away from each other. 

If you mean the coupled track in a differential pair, you should use the edge-coupled microstrip or edge-coupled stripline (your calculator doesn't seem to support asymmetric edge-coupled stripline, so you'll need to find a new calculator) to calculate the geometry for your differential pairs.