I was thinking that maybe it has something to do with the contrasts I'm setting up (in bold). I'm going to trying forming the contrasts without white space and see if this helps.

#pipeline for RNAseq GSVA analysis

##install libraries
#source("https://bioconductor.org/biocLite.R")
#biocLite("GSVA")
##

#load libraries
library(limma)
library(EGSEA)
library(org.Hs.eg.db)
library(GSEABase)
library(snow)
library(rlecuyer)
library(edgeR)
 
##make_unique(df)
#usage: analysis_ready_data <- make_unique(data_frame)
#converts ensembl to entrez id and collapses redundant ids by greatest IQR
make_unique <- function(input.data) {
 #annotate entrez id
 input.data <- data.frame(cbind(input.data, entrez=as.numeric(mapIds(org.Hs.eg.db, keys=gsub("\\..*","",rownames(input.data)), column="ENTREZID", keytype="ENSEMBL",multiVals="first"))))
 #remove NA
 input.data <- input.data[!is.na(input.data$entrez),]
 #parse duplicated entrez id
 id.dup <- input.data[duplicated(input.data$entrez) | duplicated(input.data$entrez, fromLast = TRUE),ncol(input.data)]
 data.dup <- as.matrix(input.data[duplicated(input.data$entrez) | duplicated(input.data$entrez, fromLast = TRUE),])
 ezid.dup <- unique(id.dup)
 data.unique <- input.data[!input.data$entrez %in% id.dup,]
 rownames(data.unique) <- data.unique$entrez
 data.unique$entrez = NULL
 #assess IQR for duplicates
 data.dup2 <- lapply(ezid.dup, function(x) {
  expr <- data.dup[id.dup == x,]
  if(is.matrix(expr)){
   sd.values <- apply(expr[,1:ncol(input.data)-1], 1, sd)
   mean.values <- apply (expr[,1:ncol(input.data)-1], 1, mean)
   CV.values <- sd.values/mean.values
   CV.values <- gsub("NaN","0",CV.values)
   expr <- expr[which(CV.values == max(CV.values))[[1]],]
  } else {
   expr
  }
 })
 #merge data
 merger <- data.frame(do.call(rbind, data.dup2))
 rownames(merger) <- merger$entrez
 merger$entrez = NULL
 eset <- as.matrix(rbind(data.unique, merger))
 return(eset)
}

setwd("~/Desktop")
#load RNAseq sets
counts.gene <- get(load("CRC_93_samples_RNASeq_expression_data.RData")[1])
counts.gene = make_unique(counts.gene)

#load omics
ftable <- read.delim("crc-omics.csv", header=TRUE,sep="\t")
factor.table <- read.delim("crc-omics.csv", header=TRUE,sep="\t")
groups <- factor(factor.table$group)
institution <- factor(factor.table$Institution)
lane <- factor(factor.table$Lane)
group.contrasts <- model.matrix(~0 + groups + institution + lane)
contrasts <- makeContrasts(
groups1 - (groups2 + groups3) / 2,
groups2 - (groups1 + groups3) / 2,
groups3 - (groups1 + groups2) / 2, levels=group.contrasts)

#input custom gene sets
gmt <- read.csv("geneset.gmt.csv",header=FALSE, row.names=1, sep="\t")
gmt$V2=NULL
gset=NULL
for (i in 1:dim(gmt)[[1]]){
 hold=NULL
 hold <- list(gmt[i,gmt[i,]!=""])
 hold <- as.character(mapIds(org.Hs.eg.db,
  keys=as.character(as.matrix(hold[[1]])),
  column="ENTREZID",
  keytype="SYMBOL",
  multiVals="first"))
 hold <- hold[!is.na(hold)]
 gset[[i]] <- hold
}
names(gset) <- rownames(gmt)

#Lei's method for voom generation
y <- DGEList(counts = counts.gene, group = ftable$factors)
table(rowSums(y$counts == 0) == ncol(counts.gene))
y <- y[!rowSums(y$counts == 0) == ncol(counts.gene),]
y2 <- calcNormFactors(y, method = "TMM")
logCPM <- cpm(y2, log=TRUE)
min.sample.size <- min(as.vector(table(ftable$factors)))
keep <- rowSums(cpm(y) > 1) >= min.sample.size
y2 <- y[keep, keep.lib.sizes=FALSE]
dge <- voomWithQualityWeights(y2,
 design=group.contrasts,
 normalization="quantile",
 plot=FALSE)
 
#generate custom geneset for analysis
gene_idx <- buildCustomIdx(entrezIDs=rownames(dge$E),
 gset,
 label="custom",
 name="Consensus_gene_sets",
 species="Human",
 min.size=1)

#egsea analysis
gsa <- egsea(voom.results=dge,
 contrasts=contrasts,
 gs.annots=gene_idx,
 baseGSEAs=egsea.base(),
 egsea.dir="~/Desktop/custom_egsea",
 sort.by="avg.rank",
 num.threads=2,
 report=TRUE)

Yea, I figured this was the problem. However how do I remove the / from the contrast, without losing the contrast? e.g., grp1-(grp2+grp3) is not the same as grp1-(grp2+grp3)/2
 

Removing the forward slash doesn't help either.

> contrasts <- makeContrasts(
+ groups1-(groups2+groups3),
+ groups2-(groups1+groups3),
+ groups3-(groups1+groups2), levels=group.contrasts)
> gsa <- egsea(voom.results=dge,
+  contrasts=contrasts,
+  gs.annots=gene_idx,
+  baseGSEAs=egsea.base(),
+  egsea.dir="~/Desktop/custom_egsea",
+  sort.by="avg.rank",
+  num.threads=2,
+  report=TRUE)
[1] "EGSEA analysis has started"
[1] "Log fold changes are estimated using limma package ... "
[1] "EGSEA is running on the provided data and custom gene sets"
The EGSEA results have been loaded from
~/Desktop/custom_egsea/custom-fisher-egsea-results.rda
If you want to re-run the EGSEA test, please remove this
file or change the egsea.dir value.
[1] "The top gene sets for contrast groups1 - (groups2 + groups3)/2 are:"
                              ID         p.adj
IMMUNE_ESTIMATE          custom2 3.888136e-184
PD1_REACTOME            custom65  1.353047e-69
IMMUNE_RESP_GO_BP       custom59 5.924559e-150
JAK_STAT_KEGG           custom32  2.778769e-46
TGFB_1                  custom10  3.449230e-39
STROMAL_ESTIMATE         custom1 7.961888e-157
MATRIX_REMODEL_REACTOME custom13 6.235033e-111
TGFB_2                  custom11  3.954068e-45
KEGG_CELL_CYCLE         custom83  4.727950e-40
IMMUNE_MDSC_CERWENKA    custom80  1.049228e-34
Writing out the top-ranked gene sets for each contrast ..CUSTOM gene sets
Error in file(file, ifelse(append, "a", "w")) :
  cannot open the connection