Intrude, obtrude, interlope, butt in are comparable when meaning to thrust oneself or something in without invitation or authorization.
Intrude both transitively and intransitively carries a strong implication of forcing someone or something in without leave, without right, or against the will of others; it often connotes rudeness, officiousness, or invasion of another’s property, time, or personal privacy.
Obtrude in this relation retains much of its basic notion of pushing or extending something into view; it may imply nothing beyond this fact or it may suggest the impropriety and objectionableness of the act or the disagreeableness of the offense.
Interlope implies an interposition of oneself in a place or position which has an injurious effect on one or both of the persons or things concerned.
Butt in implies an abrupt or offensive intrusion suggestive of the manner in which a horned animal attacks its enemy; in this sense the term usually suggests absence of ceremony, a sense of propriety, or decent restraint.