The explanations in the Duden partly reference each other — it doesn’t help much to know that irgendwo means an irgendeinem Ort when you also don’t understand irgendein.
Irgend is used to reinforce uncertainty similar to some/any.
Hat irgendwer meine Tasche gesehen?
Has anyone seen my bag?
Kannst du es irgendwo sehen?
Can you see it anywhere?
Sie suchen irgendwas.
They're looking for something.
Regarding the differences you're interested in:
irgendwas and etwas are synonyms. like the example above could also be written as:
Sie suchen etwas.
Irgendeine and einige however are quite different. Einige is used for small groups. Example:
Es gibt einige mögliche Übersetzungen.
There are several possible translations.
Irgendeine, as said at the beginning, just expresses uncertainty. Example:
Gibt es irgendeine Lösung?
Is there any solution?
Most of the time, irgend- corresponds to no matter who/which/where/how/... or I don't know the details.
- irgendjemand, irgendwer -> some/any person (I don't know or don't care who)
- irgendwo -> at some/any place, no matter where
- irgendein Auto -> some/any car, no matter which one
- irgendwelche Insekten -> some/any insects, no matter which kind
- irgendwas, irgendetwas -> something (I don't know what)
Note that irgend- is sometimes redundant. There is no fundamental difference between Hat jemand angerufen and Hat irgendjemand angerufen or between Hast du ein Taxi gesehen and Hast du irgendein Taxi gesehen; irgend- just stresses the idea of "I don't care who/which" which is already expressed in the base word.