First of all, OLS is an estimation technique, not a model. I will assume you have a linear regression model that you would like to estimate using OLS.
Regarding non-stationarity, it is not covered under the OLS assumptions, so OLS estimates will no longer be BLUE if your data are non-stationary. In short, you do not want that. Also, it does not make sense to have a stationary variable explained by a random walk, or vice versa. A stationary process will revert to its mean while an integrated process may wonder off and away, hence the two are no match for each other. This situation is known as an unbalanced regression. (Although having variables of different orders of integration in the same regression equation can make sense when there is cointegration.)
Regarding seasonality, it is also a form of non-stationarity and you should model it explicitly. When ignored, seasonality may result in undesirable outcomes and misinterpretations. For example, you may find a statistically significant relationship between two variables when the only common underlying relationship between them is seasonality; think about modelling how weather depends on ice-cream sales.
You should care about specifying the model correctly (or, more realistically, as well as you can) first and then choosing an estimation method. Perhaps your dependent variable is stationary while GDP is not stationary; then you normally cannot model how the first depends on the second; but perhaps it makes sense to ask how your dependent variable depends on changes in GDP (the first differences of DGP). Also, if you have seasonality, include some terms to account for it or adjust the data for seasonality before putting the variables into the model.
Also, keep in mind that you are working with a pretty small sample (40 observations). The asymptotic properties of your estimators may not be that relevant yet; there is little room for constructing a rich model. I'm not sure if you can do much about it, but that's a different topic.