How to find out if there is a relationship between 6 independent variables and 3 dependent variables Let me apologise for being so new to statistics, and ask for your patience and expertise in helping to achieve the following.
We would like to ascertain the extent to which any or any combination of the following have an effect on whether customers tend to be “Paid in full”, “In Arrears” or have made “No Payments” at all:
1.  Credit Score 
2.  Length at job
3.  Length at Residence
4.  Number of CCJs
5.  Total Monthly Income
6.  Loan Amount (Capital)
There are 3 dependent variables:
Paid in full – a customer who is keeping up with payments and therefore not in arrears. We can classify this type of behaviour as a customer who “can pay”.
Behind – a customer who is paying something but not enough towards the agreement and therefore in arrears.  We can also classify this type of behaviour as a customer who “can’t pay”.
No pay – a customer who has not paid anything towards their agreement.  We can also classify this type of behaviour as a customer who “won’t pay”. 
So, we need to find out the relationship between the 6 respective independent variables above and the 3 dependent variables (Paid in full, Behind or No Pay).  There could be independent causality, or causality may result from a combination of the variables.
Here is an example of the type of information we are looking for – the correlation analysis might reveal having a credit score of 450 – 550 means you are more likely to have paid your unsecured loan, but a score above 551 shows no correlation.  Or, another example could be, if your total monthly income is less than 800 you more likely to have not paid.  We need to know if there is any relationship that may exist from multiple independent variables.  For example, the analysis might show a customer with a credit score of 300-350 with 2 or more CCJs and a total monthly income of 700 – 800 is likely to be “Behind” on payments
I have an excel sheet with data in it, which has the following headings:
Unique ID, Paid in Full, Behind, No Pay, Capital borrowed, credit score, length at residence, length at job, number of CCJs, total monthly income.
A "1" will only ever exist in one of these three columns – Paid in Full, Behind, or No Pay. The “1” indicating whether a customer has paid in full, is behind, or not paid anything towards the agreement.
This layman would really appreciate your help on achieving this, or guidance.
Thank you.
 A: A quick side note, it might be better to refrain from discussing causality until you have a solid correlation and a credible explanation as to why this correlation can be interpreted as causality.
To start familiarizing yourself with the data, I recommend doing some mean/proportion comparisons for all your independent variables with each of your three outcomes. This will help you get a first glance at some of the relationships between your independent and dependent variables. 
You can also compare the outcomes of ad-hoc categories created based on your experience/knowledge of the context. Trying a wide range of categorizations might help you come up with ways to deal with non-linear effects which your sentence "the correlation analysis might reveal having a credit score of 450 – 550 means you are more likely to have paid your unsecured loan, but a score above 551 shows no correlation. " Again, this kind of technique can be useful if it is grounded on actual knowledge of the context, otherwise it is just data mining in its worst form.
You mentioned having three dependent variables but in fact you have just one ordinal variable with three outcomes. The basic models to deal with this kind of data are extensions of the probit and logit models to more than two outcomes: the proportional odds model or ordered logit and the ordered probit. 
The key assumption of these models is that the change in the odds (or probability) from any pair of neighboring outcome is proportional, which in your case might not hold.
You can do a rough test of the validity of that assumption in the case of your data by running two separate binary outcome regressions, (with sample limited to outcomes 1 and 2 in the first and outcomes 2 and 3 in the second) and comparing coefficients as well as the overall fit of the model. 
If the assumption does not appear credible, a simple way to solve it (although it means a loss of information) is to group two of the outcomes together. Otherwise, there exists more complicated models to treat this issue but I'm not sure using those "as a layman" is the best solution for you.
Finally, you could consider that credit issues are a selection and that the final decision is whether to try and pay it in arrears or simply stopping payment. The most standard way to model this kind of problem is the Heckman-Selection method coupled with either a probit or logit model.
As you can see, the options are endless and mostly depend on the properties of your data and the way you wish to analyze it. So again, I recommend using as much descriptive statistics as you can to know your data better, and then think long and hard about what question you want to try and answer.
