• Have clinically or pathologically confirmed diagnosis of unresectable and metastatic melanoma, cutaneous SCC, basal cell carcinoma, Merkel cell carcinoma, high-grade bone and soft tissue sarcoma or HER2/neu (-) breast cancer with no curative treatment options.

• The unresectable disease to be irradiated and injected with medications must be located in breast, dermal, subcutaneous, or soft tissue, or lymph nodes with the longest axis of the tumor 2-7 centimeters, and should be considered safe for injection by the investigator.

• The metastatic disease must be measured per irRECIST criteria.

• Patient must have lesion that can be biopsied and is willing to undergo the procedure as part of the protocol.

• Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 1.

• Participants of child-bearing potential and men must agree to use adequate contraceptive methods (e.g., hormonal or barrier method of birth control; abstinence) prior to study entry. Should a woman become pregnant or suspect she is pregnant while she or her partner is participating in this study, she should inform her treating physician immediately.

• For patients with history of radiotherapy to the same location that will be treated on study, he/she will be eligible only if the prior radiation dose was under or equal to 68 Gy total and delivered more than 6 months prior to planned re-treatment. (The cumulative dose received to the irradiated area will be no more than 87 Gy total, including a maximum of 68 Gy allowed from prior treatment course.)

• Patient requires the use of radiation therapy to the target lesion of palliation of symptoms and/or achieving local control as part of standard of care as deemed appropriate by treating radiation oncologist.

• Patients must agree to radiation to the tumor.

• Any line of therapy allowed, radiologically or clinically confirmed progression on prior therapy

• Must have adequate organ and marrow function present as defined below:

‣ Platelets \>= 100,000/uL

⁃ Hemoglobin \>= 8.0 g/dL

⁃ Absolute neutrophil count (ANC) \>= 1500/uL

⁃ Total bilirubin =\< 1.5 X institutional upper limit of normal (ULN)

⁃ Aspartate aminotransferase (AST) (serum glutamic-oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 2.5 X institutional ULN.

⁃ Creatinine =\< 1.5 X ULN OR creatinine clearance \>= 50 mL/min per Cockcroft-Gault equation for patients with creatinine levels greater than ULN.

• Participant or legal representative must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure.

• Patients must agree to injections of CDX-301, CDX-1140, and poly-ICLC.

• Patients must agree to appropriate clinical monitoring to receive the study regimens.

• Patients must agree to photos of tumors and use of the photos for publication.

• Patients should have an administration site for all injections that is free of potentially complicating dermatologic conditions such as rashes.