I intend to use voom+limma to analyse an RNA knockdown experiment that essentially looks like this:

design <- data.frame(gene=c(rep("control", 2), rep("gene1", 6), rep("gene2", 6), rep("gene3", 6)),
                     oligo=c(rep("control", 2), paste("oligo", c("a", "a", "b", "b", "c", "c",
                                                                  "d", "d", "e", "e", "f", "f",
                                                                  "g", "g", "h", "h", "i", "i"))))

For each target gene I have multiple oligos to control for off target effects. In addition I have non-treated controls. 

For each target gene, I would like to identify genes that are DE in all the corresponding oligos. I know I can simply do it using a model matrix like this:

mod <- model.matrix(~oligo)

This way I can test for an effect of each oligo separately using the coefficients. Then I can extract all DE genes (i.e. using decideTests) and then only keep genes that are DE in all tested coefficients for each gene.

Is there a more elegant way to express this approach as a single contrast for each gene?

Other suggestions for design and contrast matrices for this type of experiment are also welcome. The actually experiment is considerably bigger, with many more genes and oligos, but this is the general design.

For your specific purpose, I don't think there's a more elegant method than what you propose. If you want genes that are DE for each oligo versus the control for a given set of oligos (presumably against the same target gene), then you'll obviously have to test each pairwise oligo-control comparison for DE, and then intersect the results. Other contrasts don't quite do the same job - for example, doing some ANOVA-like comparison would reject the null if any of the oligos were significantly different from the control, and similarly, comparing the average expression of the oligo groups against that of the control doesn't guarantee that each oligo is significant. 

So, I would stick with a one-way layout, and perform pairwise comparisons between each of the oligo groups against the control group. As for the intersection itself, there's a couple of ways to do it:

• The quick-and-dirty approach is to take the DE list of each oligo-control comparison at the relevant FDR (e.g., 5%, using decideTests), and then take the intersection of the lists across multiple comparisons. 
• The more rigorous approach is to, for each gene, take the maximum p-value across all oligo-control comparisons of interest. This represents the p-value from an intersection-union test (see various work from Berger, e.g., here), and you can then apply the BH method to those p-values to control the FDR across all genes.

The second approach provides a better guarantee of error control, while the first approach is more intuitive - but I'd imagine that both should be fairly similar in your case where there (hopefully) should be strong correlations between oligos targeting the same gene. It's probably wise to check that each knockdown was successful, otherwise your intersection would be empty if any oligo had no DE genes.