The purpose of the research is to explore the dynamic multiscale linkage between economic policy uncertainty, equity market volatility, energy and sustainable cryptocurrencies during the COVID-19 period. We use a multiscale TVP-VAR model considering level (EPUs and IDEMV) and returns series (cryptocurrencies) from 1 December 2019 to 30 September 2022. The data are then decomposed into six wavelet components, based on the wavelet MODWT method. The TVP-VAR connectedness approach is used to uncover the dynamic connectedness among EPUs, energy and sustainable cryptocurrency returns. Our findings reveal that CNEPU (USEPU) is the strongest (weakest) NET volatility transmitter. IDEMV is the most consistent volatility NET transmitter among all uncertainty indices across the original returns and wavelet scales (D1~D6). Energy cryptocurrencies, i.e., GRID, POW and SNC, are more likely to receive volatility spillovers than sustainable cryptocurrencies during a turbulent period (COVID-19). XLM (XNO) is least (most) affected by volatility spillover in system-wide connectedness, and XLM (ADA and MIOTA) showed a consistent (heterogeneous) non-recipient behavior across the six wavelet (D1~D6) scales and original return series. This study uncovers the dynamic connectedness across multiscale, which will support investors considering different investment horizons (D1~D6).