Connections between different theories of personality There are a several theories on personality: the Big Five personality traits, Watson en Clark's extraversion en neuroticism, Grey's Behavioural Inhibition &amp; Behavioural Activation (BIS/BAS), Eysecks Psychotocism, Extraversion and Neuroticism (PEN) model, the Socionics &amp; Information Metabolism theory discussed in this related question, the list goes on.

But are there any theories proposing 'translations' from a personality described according to one theory, to the same personality described according to one of the others? 

I would expect that this translation would be mediated through latent variables. 
However i have not found any research that does this, while there are papers on the relatioships between test-results. That is, there is empirical research that describes the correlations between the scores on questionnaires that are designed to measure personality according to different theories.

For example: From BIS/BAS to the big five - Smits and Boeck - European Journal of Personality Vol 20, no 4, 255–270

The reason i ask, is because i have a dataset of some 460 subjects who took several personality questionnaires (big 5 as well as BIS/BAS), in addition they completed the Adjective Check List (ACL). Test subjects also did tests which measure impulsiveness: a Response Inhibition task, a Reversal Learning task and the Balloon Analogue Risk Task.

I think it would be interesting to compare a model based on literature to the correlations found in this dataset. 
Specifically i would try to predict certain approach/avoidance measurements (test-subjects also completed an approach-avoidance task) from the rest of the test data and the theoretical connections between the different factors that are supposed to underlie the measurements.

Other related questions:

What is the support for a global personality factor?

What is understood about interactions between personality types or traits?
It's unclear if the idea of 'translation' from one personality framework to another is a meaningful concept. A score on any given personality factor represents some weighted combination of measures - usually endorsement of questionnaire items like "I am the life of the party", etc.

As such, every factor score is a unique variable that probably doesn't reflect some underlying property of the human brain, but is a scientifically convenient construct 

Though personality theories are usually based on how different trait scores factor analyse, and so they often have a lot of overlap. Eysenck's Neuroticism and Extroversion factors are very similar to the Big Five N and E factors, because those emerge very strongly when you look at the common clusters of human traits. But they aren't identical, because they're comprised of different items and exist in a different multidimensional test structure with different cross-loadings.

The different theories are different because they cannot be translated to one another, though similarities can always be drawn.