Dry-electrode Motor Imagery Electroencephalography (MI-EEG) enables fast, comfortable, real-world Brain Computer Interface by eliminating gels and shortening setup for at-home and wearable use.However, dry recordings pose three main issues: lower Signal-to-Noise Ratio with more baseline drift and sudden transients; weaker and noisier data with poor phase alignment across trials; and bigger variances between sessions. These drawbacks lead to larger data distribution shift, making features less stable for MI-EEG tasks.To address these problems, we introduce STGMFM, a tri-branch framework tailored for dry-electrode MI-EEG, which models complementary spatio-temporal dependencies via dual graph orders, and captures robust envelope dynamics with a multi-scale frequency mixing branch, motivated by the observation that amplitude envelopes are less sensitive to contact variability than instantaneous waveforms. Physiologically meaningful connectivity priors guide learning, and decision-level fusion consolidates a noise-tolerant consensus. On our collected dry-electrode MI-EEG, STGMFM consistently surpasses competitive CNN/Transformer/graph baselines. Codes are available at https://github.com/Tianyi-325/STGMFM.