Just to add, it looks to me as if all but one of the segments of the Sentiero Azzurro (Blue trail: SVA n. 2) are closed. According to the park website, Monterosso to Venazza is open but the other three are not. You can see the map by clicking on the link below (red lines mean closed) and note that the last entry on the chart (SVA (ex n.2) Riomaggiore - Vernazza) has a red dot - which also means closed.
http://www.parconazionale5terre.it/sentieri_parco.asp?id_lingue=1
Ken is right that, other than Via dell' Amore - which you won't be able to do anyway, "walking" is not a great descriptor for the trails. Monterosso to Vernazza is a nice "hike" but a fairly strenuous one if you're not much of a trekker to begin with. Still, there are some wonderful views from that path. Unfortunately, due to the closure of the rest of the Sentiero Azzurro, I'd also expect it to be completely mobbed.
There's going to be little difference between August and September: it's going to be very busy. The #1 thing to do is just explore the villages: stop into the churches; climb up to the overlooks (some of the cemeteries afford excellent views); do some people watching; take a ferry ride; and shoot loads and loads of pictures.