This is not by any means pretty code, but it should work for you and output it in tab delimited format in a file in your output directory. You can then re-read that into R using read.table() with sep set to \t. I didn't include the decreasing order since it is late here, but with a little imagination, you could probably add it.

transformMyMatrix <- function(mymatrix, outputFile) {
        for(i in 1:nrow(mymatrix)) {
                temp <- paste(c("pos(", mymatrix[i, "pos"], ")"), collapse='')
                for(j in 2:ncol(mymatrix)) {
                        if(!is.na(mymatrix[i,j])) {
                                temp <- c(temp, paste(c(names(mymatrix)[j], "(", mymatrix[i,j], ")"), collapse=''))
                        }
                }
                write.table(t(as.matrix(temp)), file=outputFile, sep="\t", append=T, quote=F, row.names=F, col.names=F)
        }
}

Then call the function:

transformMyMatrix(mymatrix, "outputFile.txt")

For example, here is what I get with that:

mymatrix
        pos  A  C  G  T  N
1   1611111 NA  1 NA 17 NA
2  99022222  3 NA 24 NA NA
3  99092333 NA  5 NA 91 NA
4 233232333  2 22 NA NA NA

transformMyMatrix(mymatrix, outputFile="newMatrix.txt")
newMatrix <- read.table(file="newMatrix.txt", sep="\t")
newMatrix
              V1   V2    V3
1   pos(1611111) C(1) T(17)
2  pos(99022222) A(3) G(24)
3  pos(99092333) C(5) T(91)
4 pos(233232333) A(2) C(22)

Be aware that if you try to read it back into R in a data frame format, it will automatically fill in empty spots with NAs if the # of columns are uneven, so you might have to address that.