  Nonlocality is a fascinating and counterintuitive aspect of Nature, revealed
by the violation of a Bell inequality. The standard and easiest configuration
in which Bell inequalities can be measured has been proposed by
Clauser-Horne-Shimony-Holt (CHSH). However, alternative nonlocality tests can
also be carried out. In particular, Bell inequalities requiring multiple
measurement settings can provide deeper fundamental insights about quantum
nonlocality as well as offering advantages in the presence of noise and
detection inefficiency. In this article we show how these nonlocality tests can
be performed using a commercially available source of entangled photon pairs.
We report the violation of a series of these nonlocality tests (I3322, I4422
and chained inequalities). With the violation of the chained inequality with 4
settings per side we put an upper limit at 0.49 on the local content of the
states prepared by the source (instead of 0.63 attainable with CHSH). We also
quantify the amount of true randomness that has been created during our
experiment (assuming fair sampling of the detected events).
