One option (that I actually strongly suspect you won't be happy with) is this:
p <- ggplot(data=top10.df, aes(x=Country, y=value)) +
geom_bar(stat="identity")+
coord_flip() +
facet_wrap(~Age)+
labs(title="Immigrants By Country by Age",x="Country of Origin",y="Population")
pp <- dlply(.data=top10.df,.(Age),function(x) {x$Country <- reorder(x$Country,x$value); p %+% x})
library(gridExtra)
do.call(grid.arrange,pp)
(Edited to sort each graph.)
Keep in mind that the only reason faceting exists is to plot multiple panels that share a common scale. So when you start asking to facet on some variable, but have the scales be different (oh, and also sort them separately on each panel as well) what you're doing is really no longer faceting. It's just making four different plots and arranging them together.