As I know, the strand-specific and unstranded library have different counting method, so does that make sense to compare the gene expression (rpkm or rpm) from the strand-specific library and from unstranded library? If yes. which normalization method is better for this. Thanks.
I think you could use a multifactor design with DESeq (R - bioconductor) by specifying a design matrix like that :
Sample condition library A untreated unstranded B untreated unstranded C treated unstranded D treated unstranded E untreated stranded F untreated stranded G treated stranded H treated stranded
and with your count matrix :
cdsFull = newCountDataSet( countTable, designMatrix )
after that follow DESeq manual at "Multi Factor Designs" section. http://bioconductor.org/packages/release/bioc/html/DESeq.html
I think edgeR has also this type of feature.