Lifetime distributions under Type-II censored scheme have been attracting great interest due to their wide application in the fields of science, reliability, economics, environmental sciences, finance, engineering, social sciences, medicine and other fields. In this paper, Bayesian and E-Bayesian estimators for the shape parameters of the odd generalized exponential inverted Weibull distribution are estimated. The Bayes and E-Bayes estimators are derived under the balanced squared error loss function as a symmetric loss function, and the balanced linear exponential loss function as an asymmetric loss function, based on a Type II censored sample. Based on informative gamma priors and uniform hyper-prior distributions, the estimators are obtained. Finally, the performance of the proposed Bayes and E-Bayes estimates is evaluated through a simulation study to show the high flexibility and potential applications of the distribution. Moreover, the results are applied to three real data sets from the COVID-19 death rate in different countries.