ListLinePlot[
    {avg, avg + dev, avg - dev},
    PlotStyle -> {Blue, None, None},
    Filling -> {1 -> {2}, 1 -> {3}}
]

ListLinePlot[
    {
        avgs[[1]], avgs[[1]] + devs[[1]], avgs[[1]] - devs[[1]],
        avgs[[2]], avgs[[2]] + devs[[2]], avgs[[2]] - devs[[2]],
        avgs[[3]], avgs[[3]] + devs[[3]], avgs[[3]] - devs[[3]]
    },
    PlotStyle -> {
        Blue, None, None,
        Orange, None, None,
        Red, None, None
    },
    Filling -> {
        1 -> {2}, 1 -> {3},
        4 -> {5}, 4 -> {6},
        7 -> {8}, 7 -> {9}
     }
]