  Screened modified gravity (SMG) and Brans-Dicke (BD) gravity are typical
examples of scalar-tensor theories with and without screening mechanisms, which
can suppress the scalar field in dense regions. In this paper, we investigate
the tests of time-varying gravitational constant $G$, gravitational dipole
radiation, and Nordtvedt effect in BD and SMG theories, respectively. We place
new constraints on these theories by combining Cassini experiment, lunar laser
ranging (LLR) measurements, and pulsar observations from PSRs J1738$+$0333 and
J0348$+$0432. We find that screening mechanism has important influence on
theoretical constraints. The strongest, second, and weakest constraints on BD
are from Cassini, pulsar, and LLR tests, respectively. The most stringent
constraint on SMG comes from LLR measurements and improves the previous best
constraint by more than seven orders of magnitude. We derive the bounds on the
cosmological evolution of the scalar background in these theories using the
time variation of $G$. The results of all tests agree well with general
relativity (GR) and give more stringent constraints on the deviations from GR.
Finally, as an example, we consider the chameleon model and derive the
constraints on the model parameters.
