Yes, you can take cod liver oil with turmeric.
Both supplements are very common, are not considered toxic, and do not interact with each other in any negative way. They can even compliment each other if you are taking them both for sore joints. The omega-3 fatty acids which are found in cod liver oil have been shown to help reduce pain in joints, whereas turmeric supplements have been shown to reduce inflammation. Both supplements are very well researched, and how they benefit the body in this way is very well understood. Both supplements also offer a number of other health benefits including reducing oxidative stress on the body, and supporting the immune system. They compliment each other quite nicely.
In fact, you could argue that taking cod liver oil with turmeric is a good idea. Many of the components of turmeric are fat soluble, so in the digestive system the cod liver oil may help with the absorption of the active components of turmeric. This is just speculation though, and there is no research to support it.
At any rate, both supplements should be taken with food to improve their absorption.
As turmeric is more like a food than a supplement, it is generally quite safe to take with anything else in reasonable quantities. The same applied for cod liver oil too in most cases. However, there are some cod liver oil manufacturers which add lots of vitamin A into their oil. These high levels of vitamin A, whilst safe on their own, can mean that taking a multivitamin is not wise. Vitamin A in high dosages can be toxic to the liver, and taking a cod liver oil high in vitamin A in conjunction with a multivitamin may cause problems.