The first transgene will be easily screened by using marker gene analysis, but in case of second, 3rd and 4th genes it may give false results (positive results), then what alternative methods could be used?
I think using multiple specific primers which have binding sites in the border of vector and inserts would help. By colony PCR you could confirm the existence of your vector with inserts. Anyway, you have to give your plasmid sequenced as the final confirmatory test.
This is totally doable. You can use a polycistronic vector such as pST39, and clone the four inserts one at a time. That means you need four steps: clone the first insert, and then clone the second insert into the plasmid generated from the prior step, and so on. You need to design your PCR primers with restriction sites according to the sites available in the multiple cloning sites of the vector. The only limitation that may be is the insert size, as @Alireza mentioned. Please see the following reference: Tan, S. (2001) A modular polycistronic expression system for overexpressing protein complexes in Escherichia coli. Protein Expression Purif. 21, 224-34.