Control compared to 4 treatment groups I'm not very strong as far as stats go, and not super familiar with this site, so I'm sorry if any formatting is wrong here. I've tried searching for this answer but I'm still lost.
I'm interested in determining if 3 new treatments (W1, W2, W3; n=100 in each W group) are similar to an established treatment (D, n=150), and different from a control (C, n=150). I have one discrete, numerical dependent variable (DV, a score out of 10). I'm a broke student, so I'm trying to do this in R as we don't have budget for SPSS, etc.
Normality is iffy (when looking at visual outputs in R via ggplot, the curve tends to be highest at lower scores - as in highest near 3 as opposed to in the actual middle at 5, again sorry if I'm reporting this in an incorrect way). BUT I've been reading that doesn't always rule out t-tests/other things that assume normality.
If I understand things right, multiple t-tests risk losing information, as this increases chances or error with each test.
Running a linear regression with dummy variables might be what I want to do, but I'm at a loss as how to do that in R.
Any help at all would be greatly appreciated, and happy to give more information if aspects are missing.
#edited to add histogram of residuals from one-way ANOVA

A classic test for multiple treatments against a baseline is Dunnett's Test. That does multiple t-tests for each treatment against the baseline group in a way that pools data from the groups and takes the multiple comparisons into account. That is implemented for example in the DescTools package. There's an example of implementation on this page. It would probably make the most sense to compare the new treatments against the established treatment rather than against the control. With your group sizes you might be able to get away with t-tests, as the critical assumption is normality of the sampling distribution of group means rather than within-group normality.
You might better use the non-parametric Mann-Whitney-Wilcoxon Test, which is almost as powerful as a t-test when normality holds and can outperform it otherwise. That's implemented in the two-sample version of wilcox.test() in R. You only have a small number of pairwise comparisons of interest (each of 3 new treatments against standard treatment, perhaps standard treatment against control), so restricting yourself to those few comparisons and using the R p.adjust() function with a "holm" correction for multiple comparisons could work well while controlling for false-positive errors.
