Differences: 干，办，做，搞，弄
我还有几件事要（办/做）are basically carry the same meaning, which is official

我还有几件事要（干）I would say this is less formal that the top one, but you can use it in most of the occasions.

他是搞计算机的 here this 搞 = 从事于（engaged in）computer business or industry

but sometimes 搞 can express negative meanings like 他把工作搞得一团糟 he screwed his work, we usually use this as a fixed collocation: 搞得一团糟

弄 usually means casual and sometimes carries bad meanings, for example：

他马上就要弄好了，不要急。casual

弄坏了 you can see this phrase as a fixed collocation, means broke something