Since more and more multimedia data associated with spoken documents have been made available to the public, spoken document retrieval (SDR) has become an important research subject in the past two decades. Following the research tendency, many efforts have been devoted towards developing indexing and modeling techniques for representing spoken documents, but only few have been made on improving query formulation for better representing users' information needs. The i-vector based language modeling (IVLM) framework, stemming from the state-of-the-art i-vector framework for language identification and speaker recognition, has been proposed and formulated to represent documents in SDR with good promise recently. However, a major challenge of using IVLM for query modeling is that a query usually consists of only a few words; thus, it is hard to learn a reliable representation accordingly. In this paper, we focus our attention on query reformulation and propose three novel methods on top of IVLM to more accurately represent users' information needs. In addition, we also explore the use of multi-levels of index features, including word- and subword-level units, to work in concert with the proposed methods. A series of empirical SDR experiments conducted on the TDT-2 (Topic Detection and Tracking) collection demonstrate the good effectiveness of our proposed methods as compared to existing state-of-the-art methods.