As
@ttocs mentioned, it’s just easier to avoid oven cleaner. It works well but it’s pretty rare to need something that strong. I have been using Nonsense from Chemical Guys for a few years now and I now just buy it by the gallon. It works great and it’s inert.
Also be careful with using dish soap for a soapy water blend. Any of it that gets onto your exterior paint will be removing any wax or sealant that you’ve applied.
The engine bay on my Mustang is pretty clean so there isn’t much point to show a before and after when I clean it next week but I have a small oil leak that I’ll be fixing on my 6.7 soon. I’ll be cleaning that engine bay after fixing it and I’ll post up a before and after of using Chemical Guys’ Nonsense, a standard soft bristle brush, and low-pressure water.
Bottom line: always use the least aggressive option first and work up from there if needed.