how do i plot many variables in one plot?

A good way to set-up a question like this is with a reproducible example (or reprex, FAQ: What's a reproducible example (`reprex`) and how do I create one?), since that'll make it much easier for folks to pick up your issues and run with it.

In the tidyverse, you might use tidyr to reshape your data, and ggplot2 to create your plot.

You have a lot of label modification options with the lhttps://ggplot2.tidyverse.org/reference/labs.html

library(tidyr)
library(ggplot2)
dt <- structure(list(
  kvartal = structure(c(15034, 15126, 15218, 15309, 15400, 15492, 15584, 15675, 15765, 15857), class = "Date"), 
  rogaland = c(5159, 4471, 4612, 4380, 4558, 4318, 4137, 4060, 4380, 4301), 
  hordaland = c(6511,6094, 5767, 5674, 5603, 5507, 5070, 4967, 5545, 5516), 
  vestagder = c(2572,2177, 2266, 2371, 2563, 2308, 2506, 2526, 2724, 2361), 
  more = c(3284, 2733, 2708, 2702, 2685, 2454, 2415, 2544, 2851, 2685)),
  class = c("spec_tbl_df", 
            "tbl_df", "tbl", "data.frame"), row.names = c(NA, -10L), 
  spec = structure(list(
    cols = list(kvartal = structure(
      list(format = "%Y-%m-%d"), 
      class = c("collector_date", "collector")), 
      rogaland = structure(list(), class = c("collector_double", "collector")), 
      hordaland = structure(list(), class = c("collector_double","collector")),
      vestagder = structure(list(), class = c("collector_double","collector")), 
      more = structure(list(), class = c("collector_double", "collector"))), 
    default = structure(list(), class = c("collector_guess", "collector")), 
    skip = 1), class = "col_spec"))

dt %>% 
  pivot_longer(rogaland:more) %>% 
  ggplot(
    aes(x = kvartal, y = value, color = name)
  ) +
  geom_line()
#> Warning: Can't combine <spec_tbl_df> and <tibble>; falling back to <tibble>.
#> ℹ Convert all inputs to the same class to avoid this warning.
#> ℹ See <https://vctrs.r-lib.org/reference/faq-warning-convert-inputs.html>.

Created on 2020-05-07 by the reprex package (v0.3.0)