A Slepian-Wolf coding scheme that can achieve arbitrary rate allocation among two encoders was outlined in the work of Pradhan and Ramchandran. Inspired by this work, we start with a detailed solution for general (asymmetric or symmetric) Slepian-Wolf coding based on partitioning a single systematic channel code, and continue with practical code designs using advanced channel codes. By using systematic IRA and turbo codes, we devise a powerful scheme that is capable of approaching any point on the Slepian-Wolf bound. We further study an extension of the technique to multiple sources, and show that for a particular correlation model among the sources, a single practical channel code can be designed for coding all the sources in symmetric and asymmetric scenarios. If the code approaches the capacity of the channel that models the correlation between the sources, then the system will approach the Slepian-Wolf limit. Using systematic IRA and punctured turbo codes for coding two binary sources, each being independent identically distributed, with correlation modeled by a binary symmetric channel, we obtain results which are 0.04 bits away from the theoretical limit in both symmetric and asymmetric Slepian-Wolf settings.