The רמ”א (סימן קל”ה ס”ב) writes אם בטלו שבת אחת קריאת הפרשה בצבור, לשבת הבאה קורין אותה פרשה עם הפרשה השיכה לאותה שבת – If the congregation did not read the parsha one week, they should read it the following week together with the parsha of that week. If the week that was skipped was a double parsha, the Mishna Berurah brings two opinions what should be done. The מהר”ם מינץ holds that the parshiyos are not lained the following week. We never find three parshiyos lained in one week. To read only one of the parshiyos the following week is also not done because אין תקנה לחצאין – we don’t fix things halfway. The same is true if the following week is a double parsha. However the הגהות מנהגים and the אליה רבה disagree. Their opinion is that both parshiyos are to be lained the following week, even though it means that three parshiyos will be lained.
However there is another machlokes that pertains to our situation. The Mishna Berurah brings from the מהר”ם מינץ that if the parsha that was not read is the last parsha of the Chumash, then it is also not read the following week. For example if Vayechi, or like this week Vayakhel Pikudei is not read, then it will not be read the following week. The reason is because the entire first parsha that is being read for the previous week together with the beginning of the regular week’s parsha is lained with one aliyah. This is because all of the olim must read from the obligatory reading of the week. It is not the proper thing to connect both seforim in one aliya. However others disagree and both parshiyos are still read the following week. The שלחן עצי שטים says that one should not protest against those that read it in this manner. The poskim say that when doing so the first oleh can end at the end of the sefer. It is not לעיכובא for him to read from that week’s laining. The שערי אפרים is of the opinion that the first three olim read from last week’s parsha and the fourth oleh reads from both parshiyos.
The Mishna Berurah (סימן תרפ”ה ס”ק ב’) brings from the שערי אפרים ורבי עקיבא איגר that if one of the four parshiyos were not read it is not read the following week. So this coming Shabbos, if we are unable to read Parshas Hachodesh, it will not be read next week. There are different opinions if it can still be read at mincha. Many are lenient to do so.
The ערוך השלחן says that the Haftarah from the previous week should also be read. I am unsure if this also applies to the haftara of the four parshiyos.
The Mishna Berurah brings a machlokes what to do if many parshiyos were missed. Some say that only the last week’s parsha that was missed is read. Others hold that all of them are read. This was the practice of Reb Nosson Adler zt”l. This depends on the two opinions mentioned above when a reading of two parshiyos was missed.
Prepared by R’ Avrohom Yehoshua Ziskind
 Sources:משנה ברורה, הקריאה בתורה והלכותיה,דרשו,פסקי תשובות