Catholic+Catholic married in Catholic Rite (Mass or wedding outside of Mass) - Valid, sacramental marriage. Indissoluble once consummated, 'until death do them part'.
Catholic+non-Catholic married in Catholic Rite -Valid, non sacramental (unless non-catholic is baptised in another tradition) married. Dissoluble, if one party is baptised (hence marriage is not Sacramental) where a person intends to enter into a sacramental marriage - needs the pope to give dispensation though so its pretty rare!
non-catholic+non-catholic married anywhere (with witnesses, unrelated, man and women ,etc) - Valid, non-Sacramental (or natural) marriage. Dissoluble under the Pauline privilege when the conversion of one party to Catholicism causes a breakdown in the marriage. Needs the local Bishop to approve.
Catholic + Catholic married in CofE or other non-catholic place (except with dispensation) - invalid - not a marriage so cannot be dissolved - get lack of form confirmed by diocese and free to marry in church. Can have marriage 'convalidated' at a later date to enter into a valid marriage in the eyes of the Church.
Catholic + non-Catholic married in CofE or non-catholic place (except with dispensation) - invalid - not a marriage so cannot be dissolved - get lack of form confirmed by diocese and free to marry within Church. May seek convalidation.
Annulments: presumed valid marriages which have other impediments. This could be anything from close family ties, murdering a partners former spouse, or a lack of intent to fulfil the wedding vows. On the last point, for instance, a pre-nuptial agreement implies the couple don't see the marriage as permanent so there would be a good case that they did not intend to be faithful until death do them part. Or want of understanding. Or severe addictions could affect one's freedom to enter a marriage. Many things could be cause for an annulment to be granted, but only the diocesan marriage tribunal (ratified by a second diocese or Rome) can issue a decree of nullity.