I want to regress
o1:o7. I would like to do the same for each of
o1:o7. Is this possible?
An excellent and very comprehensive answer has been given here to a related question. In summary, given the low number of samples, you will suffer from an inability to estimate parameters in a multiple regression. To estimate all the parameters, you will need k+2 samples to get parameter estimates with confidence intervals, or at least 9 samples for 7 predictors.
To your more general question of "can regression be of help", I would recommend you refine what exactly you mean. Do you mean help to predict v1 for new samples? Do you mean estimating parameters with a certain level of confidence? Etc. I think you will find better quality assistance with a more refined question.