Nigerian Pidgin is an English-derived contact language and is traditionally an oral language, spoken by approximately 100 million people. No orthographic standard has yet been adopted, and thus the few available Pidgin datasets that exist are characterised by noise in the form of orthographic variations. This contributes to under-performance of models in critical NLP tasks. The current work is the first to describe various types of orthographic variations commonly found in Nigerian Pidgin texts, and model this orthographic variation. The variations identified in the dataset form the basis of a phonetic-theoretic framework for word editing, which is used to generate orthographic variations to augment training data. We test the effect of this data augmentation on two critical NLP tasks: machine translation and sentiment analysis. The proposed variation generation framework augments the training data with new orthographic variants which are relevant for the test set but did not occur in the training set originally. Our results demonstrate the positive effect of augmenting the training data with a combination of real texts from other corpora as well as synthesized orthographic variation, resulting in performance improvements of 2.1 points in sentiment analysis and 1.4 BLEU points in translation to English.