If an astronaut got stuck in the middle of a space station, can he propel himself towards a wall by blowing air out of his mouth?

Just a naive and very approximate calculation:

If you neglect friction, google that human lung capacity is around $6text{l}$, air density around $1text{kg m}^{-3}$, take the inhalation time $6text{s}$ and approximate that the nostrils have area around $1text{cm}^2$, then the velocity of inhaled air will be $frac{6text{l}=6000text{cm}^3}{6text{s}cdot 1text{cm}^2}=10text{m s}^{-1}.$ The momentum transferred on inhalation is thus around $10text{ m s}^{-1}cdot 0.006text{m}^3cdot 1text{kg m}^{-3}=0.06text{kg m s}^{-1}.$

The same computation on exhalation with duration $0.5s$ gives $0.72text{kg m s}^{-1}$. The momentum gained is thus $0.66text{kg m s}^{-1}$, which for man of weight $66text{kg}$ gives you velocity $0.01text{m s}^{-1}$.

So on one breath you would reach the wall (assuming you are in the middle and have a distance around $2text{m}$ to go) in $200text{s}=3text{min}20text{s}$.

Now, you can make a breath each $7text{s}$, which adds another $0.01text{m s}^{-1}$ to your velocity. Thus the distance traveled is $$7text{s}Rightarrow 7text{cm}$$ $$14text{s}Rightarrow 7text{cm}+14text{cm}$$ $$21text{s}Rightarrow 7text{cm}+14text{cm}+21text{cm}$$ And so on. From this the time for traveling distance $2text{m}$ is around $50text{s}$.