"I drank too much at the party."
It is really more complicated than that. "Sugiru" is a verb that translates to a range of English verbs with the general sense of "going beyond." As a suffix "--sugiru" has the sense of "doing to excess" and attaches to the same form of the verb as "-masu." (nomu + sugiru = nomisugiru, "drink too much"). This is a straightforward compound verb and "--sugiru" can be attached to just about any verb with which it makes sense, e. g., tabesugiru.
Yes, "sugi" is used as a noun but you generally will not find it in a dictionary because it is actually the conjunctive stem (renyookei) of "sugiru." The use of the conjunctive form as a noun is not uncommon but it is not always idiomatic. You have to know which verbs are used this way.
は does not imply that the preceding phrase is a subject. は sometimes marks a noun as the subject, but most of the times it is used as either contrast or setting the topic of the sentence. The は in パーティーでは is used for either marking contrast or thr topic, but never the subject, as it is a phrase rather than a noun.
Even in English "at the party" is not an object. It is a clause complementing the verb. Same for Japanese that パーティーで is a complement rather than an object. で marks the location where the action takes place.
Now パーティーでは飲み過ぎた translates to "At the party, I drank too much." "At the party" should go in front of the sentence if は is used to make it the topic.