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.