Multiterminal (MT) source coding refers to separate lossy encoding and joint decoding of multiple correlated sources. This paper presents two practical MT coding schemes under the same general framework of Slepian-Wolf coded quantization (SWCQ) for both direct and indirect quadratic Gaussian MT source coding problems with two encoders. The first asymmetric SWCQ scheme relies on quantization and Wyner-Ziv coding, and is implemented via source-splitting to achieve any point on the inner sum-rate bound for both direct and indirect MT coding problems. In the second symmetric SWCQ scheme, the two quantization outputs are compressed using multilevel symmetric Slepian-Wolf coding. This scheme is conceptually simpler and can potentially achieve most of the points on the inner sum-rate bound. Our practical designs employ trellis coded quantization, LDPC code based asymmetric Slepian-Wolf code, and arithmetic code and turbo code based symmetric Slepian-Wolf code. Simulation results show a gap of only 0.24-0.29 bit per sample away from the inner sum-rate bound for both direct and indirect MT coding problems.