In this paper, we investigate the characteristics of bright-like solitons, flat-topped solitons, and gray solitons in nonlocal nonlinear fused coupler. Firstly, the fundamental bright-like solitons with different parameters are obtained by the Newton iteration. It is found that the peak value and beam width of the ground state bright-like soliton increase with the enhancement of the nonlocality degree and nonlinear parameter, and they decrease with the propagation constant increasing. The power of the ground state bright-like soliton increases with the increase of the nonlocality degree and the width of coupling function, and it decreases with the propagation constant increasing. These numerical results can also be verified in the case of multipolar bright-like solitons. Secondly, by changing the coupled mode, the solutions of multipolar bright-like solitons, flat-topped soliton and grey solitons are obtained. The transmission stability of multipolar bright-like solitons, flat-topped soliton and grey solitons are studied. The stability of solitons is verified by means of linear stability analysis and fractional Fourier evolution. In the process of long-distance propagation, the propagation of bright-like solitons, gray solitons, and flat-topped soliton with one to three-pole symmetric peaks are stable, and the tripolar bright-like solitons with different soliton peaks and tripolar gray solitons are unable to transmit steadily. At the same time, it is found that the gray soliton with three poles or more is not easy to maintain its transmission stability. It is also found that the higher the grey scale of the gray soliton, the easier it is to realize stable transmission. Finally, it is found that the coupling function width not only affects the power of the soliton, but also realize the conversion among different soliton structures by adjusting the coupling function width.