Who to contact when inbound to adjoining class deltas?
You should contact the tower of the Delta you intend on transitioning through/entering first. Tell them you want to transition through their airspace. If they clear you to enter their airspace you can request a frequency change while still inside the first delta and contact the second. This is the same procedure as say departing a Delta that abuts a Bravo then taking a Bravo transition. You could also ask for a handoff to the second delta from the controller at the first. 

For example I fly out of KPNE often a Delta abutting a Bravo, if I want to fly south through the bravo before take off I can call the tower with something along the lines of, 


  "Archer 123PB holding short at 33 ready for departure to the south to KWWD.
  Can I get a bravo handoff as well?"


An example in your case might be


  Camarillo tower, Piper 123PB 5 miles to the east looking to transition through your airspace to KOXR


The tower may respond with 


  Piper 123PB approved as requested maintain 1500 ft. hold course and overfly the field


Then as you are a bit more east (most likely past the field in this case) 


  Camarillo tower requesting frequency change 


Tower


  Frequency change approved 


You can then call OXR with 


  Oxnard tower Piper 123PB 3 miles to the east inbound for a landing at OXR with information {current AITS}


This is going to happen fast and you will need your frequencies in hand for this. You can ask the first tower for a handoff which they may orchestrate but you should be prepared for both options. If you have some kind of a pre-programmable radio this is a great example of where queueing up your frequencies will help. 

Your other option (in this specific case) weather permitting you could overfly KCMA above 2000 ft. since the delta ends at 2000 Ft. and simply request entrance to the second delta. In this case you never actually enter the first delta and no clearance is required. 

In some cases, there are prior agreements that may not match the charts for adjacent airspaces.