Basically, yes. You'll need to strip all the paint off. What will happen is simple. The old paint will continue to let go and peel, even with new primer and paint over top of it. In fact, when introducing new paint to old paint, there is a chemical reaction gonna take place, especially in oil-based paints to create tooth for them to knit to each other. The old paint becomes worse and let's go even more so, than doing nothing to it.
It's a nice sign, and I can't tell what kinda wood it is, but once you strip it, it will need to be filled and a good thick primer would be advisable and water-based will be alright. Don't get a primer & sealer all in one, just primer.
Oh, and same goes for the birds. A tooth brush or small wire brush will work to get in all the feathers and stuff.