How can I reduce street noise behind my house?
To provide even a little noise reduction, you need to eliminate air gaps in the fence.   If wind can blow through, sound can come through too.  There is little you can do to improve the fence without first sealing the gaps.   Adding foliage (i.e. shrubs or vines) will do nothing.

To seal the gaps you need to 

After sealing the gaps, the next steps would be to increase the barrier height and/or adding mass to the barrier (usually done by adding extra layers)

Here are some US govt documents related to barriers.


http://www.fhwa.dot.gov/environment/noise/noise_barriers/design_construction/keepdown.cfm
http://ntl.bts.gov/lib/35000/35700/35778/FHWA-EP-00-005.pdf