"I agreed with them" might imply that they suggested it and I agreed, which is not what it means. "I reached an agreement with them" is wordy and tends to imply a process of negotiation, which is not likely to have been involved. "They and I agreed" or "I and they agreed" would be accurate, I think, but why not just "we agreed"? Much neater, and I don't think there is any possibility of ambiguity.

Marriages can be solemnized, but that usually implies a religious ceremony. The more neutral word is "perform". And it should be "the marriage": the one this is all about. It just means the preliminaries are in order, so let's get on with it.

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Note added at 4 hrs (2016-07-30 22:57:10 GMT)
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Oliver accuses me of unacknowledged ignorance and conceit for failing to agree with him that "perform a marriage" is incorrect. I have no taste for exchanging insults, but I insist that both "perform a marriage" and "perform a marriage ceremony" are correct and that the substance of the objection has no foundation. As I said in the first place, the word "marriage" can mean a marriage ceremony, so the two expressions are synonymous:

"marriage
1. the state or relationship of living together in a legal partnership
2. a. the legal union or contract made by two people to live together [...]
3. the religious or legal ceremony formalizing this union; wedding"
http://www.collinsdictionary.com/dictionary/english/marriage

"1 a (1) : the state of being united to a person of the opposite sex as husband or wife in a consensual and contractual relationship recognized by law
(2) : the state of being united to a person of the same sex in a relationship like that of a traditional marriage <same-sex marriage> b : the mutual relation of married persons : wedlock
c : the institution whereby individuals are joined in a marriage
2: an act of marrying or the rite by which the married status is effected; especially : the wedding ceremony and attendant festivities or formalities"
http://www.merriam-webster.com/dictionary/marriage

Therefore a marriage, in the sense of a wedding ceremony, can be performed, and not surprisingly this usage is found in many official sources. Here are a couple to illustrate the point, one from the US and one from the UK:

"Section 551.51, supra, has a proviso which permits a probate judge of any county of the State of Michigan to perform a marriage under the conditions set forth in section 551.202 of the Compiled Laws of Michigan, as amended June 30, 1967, Public Act No. 175, where one or both of the parties are under the age of consent."
https://www.justice.gov/sites/default/files/eoir/legacy/2012...

This UK example shows that "perform a marriage", without ceremony, is not new:

"Certificate to perform a marriage.
Date: 12 March 1861"
http://discovery.nationalarchives.gov.uk/details/rd/835a898a...

Of course "perform a marriage ceremony" is perfectly correct also. I have to say I think it is absurd to be arguing about this.