Voltage Spikes in MOSFET H Bridge
There are three main causes for what you are seeing, which one or combination is dependant on specifics of your setup

Probe pickup

There is the possibility these spikes are not real &amp; are artefacts of how you are probing.  If you are using a x10 or x100 probe then the clip is EARTH referenced. If you are connecting this to the SOURCE of the lower FET this will not be the same EARTH as the scope &amp; thus there will be some bounce. 

Not the same EARTH? but the circuit indicates the SOURCE of Q2, Q4 are EARTH. In practice they are not simply due to stray inductance - not all earths are equal.

It could pickup due to a loop you created at the point of measurement.   

Poor powercore layout

Below is what you believe your layout is ( I have added the DCLink capacitor because I really hope you have one...) 



In practice it is slightly different 



In physically constructing your H-Bridge you may have chosen convenience in placement of suitability of flow. The stray inductance in RED are some that will compound switching overshoots as you force commutate the current.

Gatedrive and device specifics

Depending on specifics of your gate-drive you maybe driving the MOSFETs too hard (gate resistor too low), the layout is poor such that the driver can't keep the device off.

Voltage overshoot is an expected byproduct of forced-commutation

Finally... there will always be some voltage overshoot because the existence of stray inductance like there will always be reverse recovery current.  Improvements in layout can improve this, slowing down switching times can equally improve it or if it really cannot be reduced... snubber circuitry can be added to dissipate the additional energy



As to why you lost control... 


  While testing after working for few minutes the fuse blew, Q1 and Q2
  failed short circuiting Drain &amp; Source.


That may or may not be related to the observed overshoots BUT aspects of your control could also contribute: deadtime, minimum pulsewidth etc.