How to address nonlinearities among covariates when modelling? Generally, it is recommended to drop one variable from modelling when we found any collinearity among two variables.
But what when two or more independent variables have nonlinear relationship. Can they all be used in same model as independent variable?
 A: 
Generally, it is recommended to drop one variable from modelling when we found any collinearity among two variables.

Recommended by whom exactly?  Collinearity between explanatory variables is a ubiquitous part of statistical modelling, and it is not generally the case that you would drop a variable just because of collinearity with another variable.  Indeed, if the advice you have stated were to be followed, we would never use more than one explanatory variable in any model.
Regression models allow you to have two or more explanatory variables that have non-zero collinearity.  So long as the set of explanatory variables are linearly independent you still get an identifiable linear model and you can estimate the relationships between the explanatory variables and the response.  Collinearity will have the effect of inflating the standard error of your estimators, and in cases where explanatory variables are strongly collinear, it is difficult to separate their "effects" and thus, the standard errors are inflated a lot.  This is not fatal to the model, and you will still often get reasonable predictions from your model in these cases.  It just means that it is difficult to demarcate the "effects" of variables that are strongly collinear.
A: Correlation among regressors is almost always the case when working with economic variables. It only becomes problematic when the variables are perfectly collinear, i.e. one regressor can be written as a linear combination of other regressors, meaning $(X'X)$ is is singular so $(X'X)^{-1}$ does not exist. If the variables are related in a nonlinear fashion, e.g. one regressor is another regressor squared, the collinearity problem is not an issue.
