We investigate the $\Lambda\Lambda$, $N\Omega$ and $K^-p$ momentum
correlations in high-energy heavy-ion collisions
and their relevance to the hadron-hadron interactions.
For $R/a_0<0$, $|R/a_0|\ll1$ and $R/a_0>1$,
where $R$ and $a_0$ denote the source size and scattering length,
the correlation functions at small relative momenta
are enhanced, strongly enhanced and suppressed, respectively,
by the interaction when the interaction range is short
and the single channel treatment is justified.
The recently observed $\Lambda\Lambda$ correlation function
is found to be enhanced by the interaction
from that by the quantum statistics and feed-down effects,
provided that the pair purity is as large as the statistical model estimate.
The scattering length of the $\Lambda\Lambda$ interaction is constrained
to be $1/a_0<-0.8~\mathrm{fm}^{-1}$ by the correlation data.
For the $\Omega^-p$ correlation,
we propose to introduce an "SL (small-to-large) ratio" of the correlation
functions for different source sizes
in order to evade the contamination by the Coulomb interaction.
In the SL ratios, the above characteristic interaction dependence is found
to be recovered. Then the SL ratio is useful to judge the sign and strength
of the scattering length and consequently the existence
of the $S=-3$ dibaryon state.
The coupling effects of the $K^-p$ and $\bar{K}^0n$ channels
are found to be important for the $K^-p$ correlation.
The outgoing wave function in the $K^-p$ channel differs from
the complex conjugate of that in the $K^-p$ scattering
due to the coupled-channel effects.
Then we may find peak and dip structures different
from those in the $K^-p$ scattering cross section,
and it would be possible to examine the interference of the $I=0$ and $I=1$
amplitudes.