You are not loading your packages correctly. org_pkg is a string (i.e. class character).
Try this instead:
library(AnnotationDbi)
library(org.Hs.eg.db)
genelist <- c("ENSG00000074800","ENSG00000116285","ENSG00000171603","ENSG00000049245")
org_pkg <- org.Hs.eg.db
entrez_Ids <- mapIds(org_pkg, as.character(genelist), 'ENTREZID', 'ENSEMBL')
Resulting in:
head(entrez_Ids)
ENSG00000074800 ENSG00000116285 ENSG00000171603 ENSG00000049245
"2023" "54206" "22883" "9341"
EDIT: Another simpler fix
genelist <- c("ENSG00000074800","ENSG00000116285","ENSG00000171603","ENSG00000049245")
org_pkg <- "org.Hs.eg.db"
library(AnnotationDbi)
library(org_pkg,character.only=TRUE)
entrez_Ids <- mapIds(eval(parse(text = org_pkg)), as.character(genelist), 'ENTREZID', 'ENSEMBL')